Past Seminars

Thu Jan 14

11:15am - Zoom
Climate Seminar
TBA
Tue Jan 12

11:15am - Zoom
Climate Seminar
TBA
Mon Jan 11

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jan 11

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Thu Jan 07

11:15am - Zoom
Climate Seminar
TBA
Tue Jan 05

11:15am - Zoom
Climate Seminar
TBA
Mon Jan 04

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jan 04

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Thu Dec 31

11:15am - Zoom
Climate Seminar
TBA
Tue Dec 29

11:15am - Zoom
Climate Seminar
TBA
Mon Dec 28

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 28

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Thu Dec 24

11:15am - Zoom
Climate Seminar
TBA
Tue Dec 22

11:15am - Zoom
Climate Seminar
TBA
Mon Dec 21

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 21

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Dec 21

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Dec 21

Math Biology Seminar

12:00pm - Via Zoom
Exploring the predictive abilities of a mathematical model of cancer immunotherapy
Jana Gevertz, The College of New Jersey
Abstract:

Mathematical models of biological systems are often validated by fitting to the average behavior in an often small experimental dataset. Here we ask the question of whether mathematical predictions for the average are actually applicable in samples that deviate from the average. We will explore this in the context of a mouse model of melanoma treated with two forms of immunotherapy: immune-modulating oncolytic viruses and dendritic cell injections. We will demonstrate how a mathematically optimal protocol for treating the average mouse can lack robustness, meaning the best treatment for the average can fail to be optimal (and in fact, can be far from optimal) in mice that differ from the average. We also show how mathematics can be used to identify an optimal treatment protocol that is robust to perturbations from the average. Time permitting, we will also explore how robustness influences the personalization of treatment protocols for individual mice.Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Fri Dec 18

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Combinatorics and Commutative Algebra

Abstract:

See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Dec 18

10:10am - Zoom
MathCEP Seminar

Thu Dec 17

11:15am - Zoom
Climate Seminar
TBA
Wed Dec 16

PDE Seminar

3:35pm - Via Zoom
PDE Seminar

Tue Dec 15

IMA Data Science Lab Seminar

1:25pm - Online
Estimation of Manifolds from Point Clouds: Building Models from Data
Barak Sober, Duke University
Abstract:

A common observation in data-driven applications is that high dimensional data has a low intrinsic dimension, at least locally. Thus, when one wishes to work with data that is not governed by a clear set of equations, but still wishes to perform statistical or other scientific analysis, an optional model is the assumption of an underlying manifold from which the data was sampled. This manifold is not given explicitly but we can obtain samples of it (i.e., the individual data points). In this talk, we will consider the mathematical problem of estimating manifolds from a finite set of samples, possibly recorded with noise. Using a Manifold Moving Least-Squares approach we provide an approximant manifold with high approximation order in both the Hausdorff sense as well as in the Riemannian metric (i.e., a nearly isometry). In the case of bounded noise, we present an algorithm that is guaranteed to converge in probability when the number of samples tends to infinity. The motivation for this work is based on the analysis of the evolution of shapes through time (e.g., handwriting or primates' teeth) and we will show how this framework can be utilized to answer scientific questions in paleontology and archaeology.

I am currently privileged to be working with Prof. Ingrid Daubechies. Before that, I completed my PhD in applied mathematics at Tel-Aviv University under the mentoring of Professor David Levin. My MSc was co-mentored by Professor. Levin and Professor Israel Finkelstein from the Department of Archaeology and Ancient Near Eastern Civilizations.

My research ranges between analysis of high dimensional data from a geometrical perspective and the application of mathematical and statistical methods in digital humanities.

Tue Dec 15

11:15am - Zoom
Climate Seminar
TBA
Mon Dec 14

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 14

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Dec 14

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Dec 14

Math Biology Seminar

12:00pm - Via Zoom
Modelling collective cell migration in neural crest
Philip Maini, Oxford
Abstract:

A very common phenomenon in biology and ecology isthe collective movement of individuals, whether thesebe birds, fish, cells, etc. This leads to the general question: Whatare the hallmarks of collective movement?In this talk, I will review an interdisciplinary study we have been carrying out over the past decade on a powerful model paradigm for collective cell migration, namely, the chick cranial neural crest. I will show how a relatively simple multiscale hybrid cellular automaton model, combined with experimental studies, can lead to new insights into the phenomenon of collective cell migration.Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Dec 14

Special Events and Seminars

11:00am - https://umn.zoom.us/j/91913586177
HA-GMT-PDE Seminar
Alejandra Gaitán Montejo, Purdue University, Indiana
Fri Dec 11

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
COVID Modeling: Testing Scenarios and Geographical Networks
Natalie Sheils, UnitedHealth Group
Abstract:

Compartmental models for epidemiological modeling are a classic tool. In this talk I will share work we did to understand the effects of various testing strategies using a straightforward SIR model. I will also cover an extension to the typical SIR model to account for geographic heterogeneity and the incorporation of mobility data.

Natalie Sheils is a research scientist at UnitedHealth Group Research and Development. She earned her PhD in Applied Mathematics from the University of Washington in 2015 and then completed a postdoctoral fellowship at the University of Minnesota School of Mathematics. Her current research includes disease modeling and applications of healthcare data. She is involved in scientific policy and previously served on the SIAM Committee on Science Policy (2018-2019) and is now on the AMS Committee on Science Policy (2021-2024).

Fri Dec 11

10:10am - Zoom
MathCEP Seminar

Fri Dec 11

Combinatorics Seminar

9:00am - Zoom ID is 941-2794-9847
Blowup algebras of sparse determinantal varieties
Elisa Gorla&nbsp;, University of Neuchâtel
Abstract:

Let X be a sparse generic matrix, i.e. a matrix whose entries are either zeros or distinct variables. A sparse determinantal variety is the locus where X does not have full rank. While determinantal varieties, i.e. degeneracy loci of matrices whose entries are distinct variables with no zeros, are in many respects well-understood, this is not yet the case for sparse determinantal varieties. However, sparse determinantal varieties have recently received increased attention, as new approaches for studying them have been introduced by Boocher (2011) and subsequently in a series of works by Conca, De Negri and myself (2015-2020). Blowup algebras - such as the Rees algebra, the special fiber ring, and the associated graded ring - are an active area of study within commutative algebra. They are algebraic objects related to the concept of blowing up a variety along a subvariety. In this talk, I will present some new results on the Rees algebra and the fiber ring of sparse determinantal varieties. Our approach makes an essential use of the theory of SAGBI bases, which I will introduce during the talk. The new results that I will present are part of a joint work with E. Celikbas, E. Dufresne, L. Fouli, K.-N. Lin, C. Polini, and I. Swanson, which was started during the collaborative conference WICA - Women in Commutative Algebra.See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Thu Dec 10

Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
The Dehn complex: scissors congruence, K-theory, and regulators
Inna Zakharevich, Cornell University
Abstract:

Hilbert's third problem asks: do there exist two polyhedra with the same volume which are not scissors congruent? In other words, if $P$ and $Q$ are polyhedra with the same volume, is it always possible to write $P = \bigcup_{i=1}^n P_i$ and $Q = \bigcup_{i=1}^nQ_i$ such that the $P$'s and $Q$'s intersect only on the boundaries and such that $P_i \cong Q_i$? In 1901 Dehn answered this question in the negative by constructing a second scissors congruence invariant now called the "Dehn invariant," and showing that a cube and a regular tetrahedron never have equal Dehn invariants, regardless of their volumes. We can then restate Hilbert's third problem: do the volume and Dehn invariant separate the scissors congruence classes? In 1965 Sydler showed that the answer is yes; in 1968 Jessen showed that this result extends to dimension 4, and in 1982 Dupont and Sah constructed analogs of such results in spherical and hyperbolic geometries. However, the problem remains open past dimension 4. By iterating Dehn invariants Goncharov constructed a chain complex, and conjectured that the homology of this chain complex is related to certain graded portions of the algebraic K-theory of the complex numbers, with the volume appearing as a regulator. In joint work with Jonathan Campbell, we have constructed a new analysis of this chain complex which illuminates the connection between the Dehn complex and algebraic K-theory, and which opens new routes for extending Dehn's results to higher dimensions. In this talk we will discuss this construction and its connections to both algebraic and Hermitian K-theory, and discuss the new avenues of attack that this presents for the generalized Hilbert's third problem.

Thu Dec 10

11:15am - Zoom
Climate Seminar
TBA
Wed Dec 09

Probability Seminar

4:00pm - Via Zoom
On the extension complexity of random polytopes
Lisa Sauermann, IAS
Abstract:

Sometimes, it is possible to represent a complicated polytope as a projection of a much simpler polytope. To quantify this phenomenon, the extension complexity of a polytope P is defined to be the minimum number of facets in a (possibly higher-dimensional) polytope from which P can be obtained as a (linear) projection. In this talk, we discuss some results on the extension complexity of random polytopes. For a fixed dimension d, we consider random d-dimensional polytopes obtained as the convex hull of independent random points either in the unit ball or on the unit sphere. In both cases, we prove that the extension complexity is typically on the order of the square root of number of vertices of the polytope. Joint work with Matthew Kwan and Yufei Zhao

Wed Dec 09

PDE Seminar

3:35pm - Via Zoom
PDE Seminar

Tue Dec 08

Dynamical Systems

2:30pm - Via Zoom
Dynamical Systems Seminar

Tue Dec 08

IMA Data Science Lab Seminar

1:25pm - Zoom
Understanding Convolutional Neural Networks Through Signal Processing
Matthew Hirn, Michigan State University
Abstract:

Convolutional neural networks (CNNs) are the go-to tool for signal processing tasks in machine learning. But how and why do they work so well? Using the basic guiding principles of CNNs, namely their convolutional structure, invariance properties, and multi-scale nature, we will discuss how the CNN architecture arises as a natural bi-product of these principles using the language of nonlinear signal processing. In doing so we will extract some core ideas that allow us to apply these types of algorithms in various contexts, including the multi-reference alignment inverse problem, generative models for textures, and supervised machine learning for quantum many particle systems. Time permitting, we will also discuss how these core ideas can be used to generalize CNNs to manifolds and graphs, while still being able to provide mathematical guarantees on the nature of the representation provided by these tools.

Matthew Hirn is an Associate Professor in the Department of Computational Mathematics, Science & Engineering and the Department of Mathematics at Michigan State University. At Michigan State he is the scientific leader of the ComplEx Data Analysis Research (CEDAR) team, which develops new tools in computational harmonic analysis, machine learning, and data science for the analysis of complex, high dimensional data. Hirn received his B.A. in Mathematics from Cornell University and his Ph.D. in Mathematics from the University of Maryland, College Park. Before arriving at MSU, he held postdoctoral appointments in the Applied Math Program at Yale University and in the Department of Computer Science at Ecole Normale Superieure, Paris. He is the recipient of the Alfred P. Sloan Fellowship (2016), the DARPA Young Faculty Award (2016), the DARPA Director’s Fellowship (2018), and the NSF CAREER award (2019), and was designated a Kavli Fellow by the National Academy of Sciences (2017).

Tue Dec 08

11:15am - Zoom
Climate Seminar
TBA
Mon Dec 07

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 07

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Dec 07

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Dec 07

Math Biology Seminar

12:00pm - Via Zoom
Mathematical model of colorectal cancer initiation
Ivana Bozic, University of Washington
Abstract:

Cancer evolution cannot be observed directly in patients, and new methodologies are needed for obtaining a quantitative understanding of this obscure process. We developed and analyzed a stochastic model of malignant transformation in the colon that precisely quantifies the process of colorectal carcinogenesis in patients through loss of tumor suppressors APC and TP53 and gain of the KRAS oncogene. Our study employs experimentally measured mutation rates in the colon and growth advantages provided by driver mutations. We calculate the probability of a colorectal malignancy, the sizes of premalignant lesions, and the order of acquisition of driver mutations during colorectal tumor evolution. We demonstrate that the order of driver events in colorectal cancer is determined primarily by the fitness effects that they provide, rather than their mutation rates. Link to Paper.Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Dec 07

Special Events and Seminars

11:00am - https://umn.zoom.us/j/98551414461
HA-GMT-PDE Seminar
Li Chen, Massachusetts Institute of Technology, Massachusetts
Fri Dec 04

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Combinatorics and Commutative Algebra

Abstract:

See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Dec 04

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Digital Health Technology for Heart Failure Diagnostic Monitoring
Julie Thompson, Boston Scientific
Abstract:

I will describe my experience working in the area of algorithm development for implantable medical devices designed to improve heart failure patient management.  Signs and symptoms have been the hallmark of clinical assessment of heart failure (HF) patients. Current HF management takes a reactive approach, relying on patients recognizing symptoms and seeking help. However, patients often do not recognize their symptoms, resulting in late identification of a worsening condition which often results in hospitalization.  HeartLogic™ monitors patients’ HF status by assessing objective information from multiple physiological trends that are associated with common signs and symptoms of HF. HeartLogic fuses information from individual trends into a single diagnostic index and alerts clinicians when the patient’s condition changes in the worsening direction, enabling more timely ambulatory remote patient management.  HeartLogic is the first and only FDA approved Heart Failure Diagnostic in implantable cardiac therapy devices with remote alert capability.

Julie is an R&D Director at Boston Scientific Corporation where she leads a team of scientists and engineers focused on developing diagnostic and therapy technology for improved cardiac patient management.  Julie joined Boston Scientific (previously Guidant Corporation) in 2001 after completing her PhD in electrical engineering at the University of Michigan.  She began her career as a research scientist focused on tachyarrhythmia algorithms, and subsequently transitioned to research management roles.  In 2005 Julie took on leadership of a team focused on developing diagnostic technology for heart failure monitoring.  She led this group through research and design of multiple diagnostic features that have been commercialized, including a novel multi-sensor diagnostic monitoring technology, HeartLogic™, proven to effectively detect early signs of worsening heart failure in patients indicated for an implantable cardiac rhythm management therapy device.

Fri Dec 04

10:10am - Zoom
MathCEP Seminar

Thu Dec 03

Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
Shock formation and vorticity creation for compressible Euler
Vlad Vicol, Courant Institute of Mathematical Sciences, New York University
Abstract:

We discuss the formation of singularities (shocks) for the compressible Euler equations with the ideal gas law. We provide a constructive proof of stable shock formation from smooth initial datum, of finite energy, and with no vacuum regions. Via modulated self-similar variables, the blow-up time and location can be explicitly computed, the geometry of the shock set can be understood, and at the blow-up time the solutions can be shown to have precisely Holder 1/3 regularity. Additionally, for the non-isentropic problem we show that sound waves interact with entropy waves to produce vorticity at the shock. This talk is based on joint work with Tristan Buckmaster and Steve Shkoller.

Thu Dec 03

11:15am - Zoom
Climate Seminar
TBA
Wed Dec 02

PDE Seminar

3:35pm - Via Zoom
PDE Seminar

Wed Dec 02

Probability Seminar

9:00am - Via Zoom
Some properties of the discrete membrane model
Alessandra Cipriani, UT Delft
Abstract:

The discrete membrane model (MM) is a random interface model for separating surfaces that tend to preserve curvature. It is a very close relative of the discrete Gaussian free field (DGFF), for which instead the most likely interfaces are those preserving the mean height. However working with the two models presents some key differences, in that in the MM the shape is driven by the biharmonic operator, while the DGFF is essentially a Gaussian perturbation of harmonic functions. In particular, a lot of tools (electrical networks, random walk representation of the covariance) are available for the DGFF and lack in the MM. In this talk we will review some basic properties of the MM, and we will investigate a random walk representation for the covariances of the MM and what it can bring forth in terms of scaling limits of its extremes.

This talk is based on joint works, partly ongoing, with Biltu Dan, Rajat Subhra Hazra (ISI Kolkata) and Rounak Ray (TU/e).

Tue Dec 01

Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
Galois symmetries of the stable homology of integer symplectic groups
Akshay Venkatesh, Institute for Advanced Study
Abstract:

There are many natural sequences of moduli spaces in algebraic geometry whose homology approaches a "limit", despite the fact that the spaces themselves have growing dimension. If these moduli spaces are defined over a field K, this limiting homology carries an extra structure -- an action of the Galois group of K -- which is arithmetically interesting.

In joint work with Feng and Galatius, we compute this action (or rather a slight variant) in the case of the moduli space of abelian varieties. I will explain the answer and why I find it interesting. No familiarity with abelian varieties will be assumed -- I will emphasize topology over algebraic geometry.

Tue Dec 01

Dynamical Systems

2:30pm - Via Zoom
Dynamical Systems Seminar

Tue Dec 01

IMA Data Science Lab Seminar

1:25pm - Zoom
Filter-decomposed Convolution in Deep Neural Networks: On Groups, Graphs, and Across Domains
Xiuyuan Cheng, Duke University
Abstract:

Deep convolutional neural networks (CNN) have been developed and applied to data on Euclidean domains as well as non-Euclidean ones. In this talk, we introduce a framework of decomposing convolutional filters over a truncated set of basis filters, which applies to the standard CNN, group-equivariant CNN, as well as convolution on graphs. The basis decomposition reduces the model and computational complexity of deep CNNs with an automatically imposed filter regularity. First, for group equivariant CNNs, a joint basis decomposition over space and group geometry achieves group equivariance in image data, including rotation and scaling groups, with provable representation stability with respect to the geometric deformation of input data. Second, the decomposed convolution on graphs provides a unified framework for several graph convolution models. The graph convolution with low-rank local filters has enlarged expressiveness to represent graph signals than spectral graph convolutions, and shows empirical advantage on facial expression and action recognition datasets. At last, when allowing the light-weighted basis layer to be adapted to varying modals in data, the decomposition also provides a new way of invariant feature learning across domains, as well as conditional image generation. Joint work with Qiang Qiu, Ze Wang, Zichen Miao, Wei Zhu, Robert Calderbank, and Guillermo Sapiro.

Xiuyuan Cheng is an assistant professor of mathematics at Duke University. Dr. Cheng is interested in theoretical and computational problems in high-dimensional data analysis and machine learning, particularly on spectral methods, kernel matrices, and neural networks. Dr. Cheng's work is supported by NSF, NIH, and the Alfred P. Sloan Foundation.

Tue Dec 01

11:15am - Zoom
Climate Seminar
TBA
Mon Nov 30

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Nov 30

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Nov 30

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Nov 30

Math Biology Seminar

12:00pm - Via Zoom
Stability problems arising in biologically motivated PDEs
Zoi Rapti, University of Illinois
Abstract:

In many biological models, including epidemic models for cholera and rabies and predator-prey models, the diffusivity properties of the various compartments may vary. In this work, we focus on situations where the mathematical model contains one diffusing compartment (PDE) that is coupled with other compartments that are modeled by ODEs. When studying the linear stability of steady states, one ends up with rational eigenvalue problems. The difficulty with these problems, from the point of view of both analysis and numerical experimentation, is that one has no apriori information as to where the spectrum of the problem might lie. Here, we show that a number of the properties of self-adjoint eigenvalue problems (including the reality of the spectrum) carry over to the operators considered in this work. Our analysis is based on the theory of Herglotz functions. Concrete applications will be demonstrated in models of rabies infection in fox populations, plant-herbivore interactions and morphogen diffusion.Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Nov 30

Special Events and Seminars

11:00am - https://umn.zoom.us/j/92939569770
HA-GMT-PDE Seminar
John Hoffman, University of Missouri, Missouri
Fri Nov 27

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Combinatorics and Commutative Algebra

Abstract:

See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Nov 27

10:10am - Zoom
MathCEP Seminar

Thu Nov 26

11:15am - Zoom
Climate Seminar
TBA
Wed Nov 25

Probability Seminar

4:00pm - Via Zoom
NU-UMN Joint Probability Seminar

Wed Nov 25

PDE Seminar

3:35pm - Via Zoom
PDE Seminar

Tue Nov 24

Dynamical Systems

2:30pm - Via Zoom
Dynamical Systems Seminar

Tue Nov 24

IMA Data Science Lab Seminar

1:25pm - Online
Multiway Tensor Analysis with Neuroscience Applications
Gal Mishne, University of California, San Diego
Abstract:

Experimental advances in neuroscience enable the acquisition of increasingly large-scale, high-dimensional and high-resolution neuronal and behavioral datasets, however addressing the full spatiotemporal complexity of these datasets poses significant challenges for data analysis and modeling. We propose to model such datasets as multiway tensors with an underlying graph structure along each mode, learned from the data. In this talk I will present three frameworks we have developed to model, analyze and organize tensor data that infer the coupled multi-scale structure of the data, reveal latent variables and visualize short and long-term temporal dynamics with applications in calcium imaging analysis, fMRI and artificial neural networks.Gal is an assistant professor in the Hal?c?o?lu Data Science Institute (HDSI) at UC San Diego, and affiliated with the ECE department and the Neurosciences Graduate program. I am part of the Neurotheory Network. Before arriving at UCSD, I was a Gibbs Assistant Professor in the Applied Math program at Yale University, with Prof. Ronald Coifman's research group. I completed my PhD in 2017 at the Technion at the Faculty of Electrical Engineering under the supervision of Prof. Israel Cohen.

Tue Nov 24

11:15am - Zoom
Climate Seminar
TBA
Mon Nov 23

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Nov 23

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Nov 23

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Nov 23

Math Biology Seminar

12:00pm - Via Zoom
Magic, Gandhi, and balding: matrix methods for stochastic dynamic programming
Jody Reimer, University of Utah
Abstract:

What unites all of the things listed in this title? You'll have to show up to find out. This work is based on the concept of tradeoffs, a central idea in ecology and evolutionary biology. For example, the evolution of life history strategies is often framed in the language of tradeoffs. Behavioural ecologists may be interested in the tradeoffs inherent in the allocation of time (e.g., between foraging and vigilance) and resources (e.g., how much energy to invest in a reproductive attempt). Conservationists and wildlife managers must also consider tradeoffs between cost, political pressures, and management goals. Stochastic dynamic programming (SDP) is a powerful and flexible method for exploring optimal tradeoffs and has been used in a broad range of applications. In the last 30 years, concomitant with the development of SDP methods in ecology and evolution, matrix methods have emerged as another powerful tool for analyzing ecological systems. I will discuss how reformulating SDP problems in matrix notation allows us to propose a novel matrix method for solving SDP models, using intuition familiar to mathematical ecologists from matrix population models. Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Nov 23

Special Events and Seminars

11:00am - https://umn.zoom.us/j/95070384420
HA-GMT-PDE Seminar
Fri Nov 20

MCFAM Seminar

7:30pm - Zoom: https://umn.zoom.us/j/99433158383?pwd=T3h6
Dynamic Shrinkage Processes
David Matteson, Cornell
Abstract:

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a globallocal framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular globallocal priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólyagamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute?by?minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the FamaFrench five?factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods. If time permits, we will also highlight extensions to change point analysis and adaptive outlier detection. Bio: David S. Matteson is Associate Professor of Statistics and Data Science at Cornell University, where he is a member of the ILR School, Computing and Information Science, the Center for Applied Mathematics, the Field of Operations Research, and the Program in Financial Engineering, and teaches statistics, data science, and financial engineering courses. Professor Matteson received his PhD in Statistics at the University of Chicago (2008) and his BSB in Finance, Mathematics, and Statistics at the University of Minnesota (2003). He received a CAREER Award from the National Science Foundation. He is currently an Associate Editor of the Journal of the American Statistical Association-Theory and Methods, The American Statistician, and Statistica Sinica. He is an elected officer for the Business and Economic Statistics Section of the American Statistical Association. He is coauthor of Statistics and Data Analysis for

Fri Nov 20

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Strange Expectations for Simultaneous Cores
&nbsp;&nbsp;Eric Stucky, &nbsp;
Abstract:

"b-cores" are a class of partitions that originally arose in the modular representation theory of the symmetric group; partitions that are simultaneously a- and b-cores are called (a,b)-cores. We discuss a Coxeter formulation of (a,b)-cores due to Williams and Thiel that allows us to define "(W,b)-cores" for any Weyl group W, as well as a quadratic form size that in type A counts the number of boxes in the Young diagram. In their original paper they used Ehrhart theory, as well as the "strange formula" of Freudenthal and de Vries, to compute the expected size of a (W,b)-core for simply-laced W. This talk is based on recent work with Williams and Thiel that reinterprets the story from their original paper somewhat to extend their results to all Weyl groups.See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Nov 20

10:10am - Zoom
MathCEP Seminar

Thu Nov 19

11:15am - Zoom
Climate Seminar
TBA
Thu Nov 19

Colloquium

10:00am - Via Zoom ID 91514486597 (contact faculty for pw)
On the Ramanujan conjecture and its generalisations
Ana Caraiani, Imperial College London
Abstract:

In 1916, Ramanujan made a conjecture that can be stated in completely elementary terms: he predicted an upper bound on the coefficients of a power series obtained by expanding a certain infinite product. In this talk, I will discuss a more sophisticated interpretation of this conjecture, via the Fourier coefficients of a highly symmetric function known as a modular form. I will give a hint of the idea in Deligne's proof of the conjecture in the 1970's, who related it to the arithmetic geometry of smooth projective varieties over finite fields. Finally, I will discuss generalisations of this conjecture and some recent progress on these using the machinery of the Langlands program. The last part is based on joint work with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne.

Wed Nov 18

PDE Seminar

3:35pm - Via Zoom
Singularity formation in incompressible fluids and related models
Jiajie Chen&nbsp;, Caltech
Abstract:

In this talk, we will discuss the self-similar singularity formation in the Hou-Luo (HL) model for the 3D asymmetric Euler equations with boundary. Several observations obtained in the analysis of the HL model have been used to study other equations. We will also talk about some features of the singularity formation in the 2D Boussinesq and 3D asymmetric Euler equations with $C^{\alpha}$ velocity and boundary that have connections to the Hou-Luos computation for the potential 3D Euler singularity. Some of the results are joint with Tom Hou and De Huang. Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Wed Nov 18

Probability Seminar

9:00am - Via Zoom
Quantitative estimates for the effect of disorder on low-dimensional lattice systems
Ron Peled, Tel Aviv University
Abstract:

The addition of an arbitrarily weak random field to low-dimensional classical statistical physics models leads to the "rounding" of first-order phase transitions at all temperatures, as predicted in 1975 by Imry and Ma and proved rigorously in 1989 by Aizenman and Wehr. This phenomenon was recently quantified for the two-dimensional random-field Ising model (RFIM), proving that it exhibits exponential decay of correlations at all temperatures. The RFIM analysis relies on monotonicity (FKG) properties which are absent in many other classical models. The talk will present new results on the quantitative aspects of the phenomenon for general systems with discrete and continuous symmetries, including Potts, spin O(n), spin glass and height function models.
Joint work with Paul Dario and Matan Harel.

Tue Nov 17

Dynamical Systems

2:30pm - Via Zoom See abstract
Dynamics of curved travelling fronts on a two-dimensional lattice
Mia Jukic, Leiden University
Abstract:

In this talk I will introduce the Allen-Cahn lattice differential equation (LDE) posed on a two dimensional lattice. It is a well-known result that this equation admits a traveling wave solution.  In the first part, I will explain the most interesting differences between the traveling waves arising from PDEs and the traveling waves arising from LDEs, such as dependence of the wave profile and the wave speed on the direction of propagation.  In the second part, I will present recent results on the  stability of the traveling wave solutions propagating in rational directions, and  show a connection between the solution of a discrete mean curvature flow with a drift term and the evolution of the interface region of a solution that starts as a bounded perturbation to the wave profile.Zoom Link: https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Nov 17

IMA Data Science Lab Seminar

1:25pm - Zoom
Fast Statistical and Geometric Distances Between Families of Distributions
Alexander Cloninger, University of California, San Diego
Abstract:

Detecting differences and building classifiers between a family of distributions, given only finite samples, has had renewed interest due to data science applications in high dimensions.   Applications include survey response effects, topic modeling, and various measurements of cell or gene populations per person.  Recent advances have focused on kernel Maximum Mean Discrepancy and Optimal Transport.  However, when the family of distributions are concentrated near a low dimensional structure, or when the family of distributions being considered is generated from a family of simple group actions, these algorithms fail to exploit the reduced complexity.  In this talk, we'll discuss the theoretical and computational advancements that can be made under these assumptions, and their connections to harmonic analysis, approximation theory, and group actions. Similarly, we'll use both techniques to develop methods of provably identifying not just how much the distributions deviate, but where these differences are concentrated. We'll also focus on applications in medicine, generative modeling, and supervised learning.

Alex Cloninger is an Assistant Professor in Mathematics and the Hal?c?o?lu Data Science Institute at UC San Diego. He received his PhD in Applied Mathematics and Scientific Computation from the University of Maryland in 2014, and was then an NSF Postdoc and Gibbs Assistant Professor of Mathematics at Yale University until 2017, when he joined UCSD.   Alex researches problems in the area of geometric data analysis and applied harmonic analysis.  He focuses on approaches that model the data as being locally lower dimensional, including data concentrated near manifolds or subspaces.  These types of problems arise in a number of scientific disciplines, including imaging, medicine, and artificial intelligence, and the techniques developed relate to a number of machine learning and statistical algorithms, including deep learning, network analysis, and measuring distances between probability distributions.

Tue Nov 17

11:15am - Zoom
Climate Seminar
TBA
Mon Nov 16

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Nov 16

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Nov 16

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Nov 16

Math Biology Seminar

12:00pm - Via Zoom
The four Cs of nonlinear network pandemic modelling: Covid-19, Causality, Clustering, and Canada.
Alain Goriely, Oxford
Abstract:

The spreading of infectious diseases including COVID-19 depends on human interactions. In an environment where behavioral patterns and physical contacts are constantly evolving according to new governmental regulations, measuring these interactions is a major challenge. Mobility has emerged as an indicator for human activity and, implicitly, for human interactions. Here, I will study the coupling between mobility and COVID-19 dynamics and show that variations in global air traffic and local driving mobility can be used to stratify different disease phases.  I will show how local mobility can serve as a quantitative metric to estimate future reproduction numbers and identify the stages of the pandemic when mobility and reproduction become decorrelated. Moreover, we can fully understand the early spread of the disease through network modelling. I will show how an application of these ideas to the province of Newfoundland ended up in front of their Supreme Court and how it helped them controlled the disease. This is joint work with Kevin Linka and Ellen Kuhl at Stanford.Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Nov 16

Special Events and Seminars

11:00am - https://umn.zoom.us/j/92810167937
HA-GMT-PDE Seminar
Zanbing Dai, University of Minnesota, Minnesota
Fri Nov 13

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
The Evolution of Basketball with Data Science
Abstract:

For the last couple of decades, most industries have grown to take advantage of the information gained from data collection. As that happened, professional sports teams started to catch on. Baseball took the lead thanks to the amount of data collected over the years, which dates to the 1800s, but a lot of other professional sports followed and put more attention to their data collection. With technological advancements, particularly high-speed cameras, storage capacities and image recognition, more dynamic sports started to collect richer and richer data. The insights derived from this data started shifting the way the game is played and the way players are evaluated. This talk will take you through the evolution of data science in basketball and give examples of how data is shifting the way teams make decisions on and off the court.

Some bio bullet points:
- From Split, Croatia
- Member of Croatian women under 16 and under 18 basketball teams that participated in European Championships.
- Both bachelor's and doctorate degree from NJIT in applied mathematics
- Member of NJIT women's basketball team during undergraduate studies with an athletic scholarship
- Ph.D. dissertation focused on computational fluid dynamics (Department of Mathematical Sciences, NJIT)
- After graduation, started working for the Philadelphia 76ers as a data scientist in research and development department. Using data to provide insights into the game of basketball to the basketball operations office, primarily to the coaching staff, focusing on on-court strategy.

Fri Nov 13

10:10am - Zoom
MathCEP Seminar

Fri Nov 13

Combinatorics Seminar

9:00am - Zoom ID is 941-2794-9847
Free resolutions of function classes via order complexes
Justin Chen, Georgia Tech
Abstract:

Function classes are collections of Boolean functions on a finite set. In 2017, a method of studying function classes via commutative algebra, by associating a squarefree monomial ideal to a function class, was introduced by Yang. I will describe this connection, as well as some free resolutions and Betti numbers for these ideals for an interesting collection of function classes, corresponding to intersection-closed posets. This is joint work with Chris Eur, Greg Yang, and Mengyuan Zhang.See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Thu Nov 12

Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
Small scale creation and singularity formation in fluid mechanics
Alexander Kiselev, Duke University
Abstract:

The Euler equation describing motion of ideal fluid goes back to 1755. The analysis of the equation is challenging since it is nonlinear and nonlocal. Its solutions are often unstable and spontaneously generate small scales. The fundamental question of global regularity vs finite time singularity formation remains open for the Euler equation in three spatial dimensions. In this lecture, I will review the history of this question and its potential connection with the arguably greatest unsolved problem of classical physics, turbulence. Results on small scale and singularity formation in two dimensions and for a number of related models will also be presented.

Thu Nov 12

11:15am - Zoom
Climate Seminar
TBA
Wed Nov 11

Probability Seminar

4:00pm - Via Zoom
NU-UMN Joint Probability Seminar

Wed Nov 11

PDE Seminar

3:35pm - Via Zoom
A Harnack inequality for weak solutions of non-elliptic equations
Max Goering, University of Washington-Seattle
Abstract:

We'll introduce a broad class of PDEs which arise from the Calculus of Variations. After producing specific examples of some PDEs that fall within this class, we will outline a Moser Iteration based argument to derive a harnack inequality for weak solutions. This demonstrates that for 0th order regularity, the aspect of "ellipticity" which is useful is the fixed homogeneity. This raises the question of whether or not some notion of convexity can be used to replace ellipticity and still recover 1st order regularity of solutions.

Tue Nov 10

Dynamical Systems

2:30pm - Via Zoom
Dynamical Systems Seminar

Tue Nov 10

IMA Data Science Lab Seminar

1:25pm - Zoom
Natural Graph Wavelet Packets
Naoki Saito, University of California, Davis
Abstract:

I will discuss how to build a smooth multiscale wavelet packet dictionary for graph signal processing. Our approach utilizes the dual geometry of an input graph organized by new non-trivial eigenvector distances. More precisely, we construct a dual graph where each node represents a Laplacian eigenvector of the input graph and each weight is an affinity measure between the corresponding pair of the graph Laplacian eigenvectors, which is typically the inverse of the non-trivial distance between them. Once such a dual graph is formed, we bipartition the dual graph and construct tree structured subspaces. Finally, we generate smooth localized wavelet packet vectors (and the expansion coefficients of an input graph signal) on each such subspace that corresponds to a collection of the graph Laplacian eigenvectors. This can be viewed as a graph version of the "Shannon" wavelet packet dictionary. Using the best-basis algorithm or its variants on this graph wavelet packet dictionary, one can select a graph orthonormal basis suitable for a given task such as efficient approximation, denoising, classification.
I will also demonstrate the effectiveness of our graph wavelet packet dictionary compared to some other graph bases (e.g., graph Haar basis, graph Walsh basis, etc.) using both synthetic and real datasets.

This is joint work with Alex Cloninger (UC San Diego) and Haotian Li (UC Davis).

Naoki Saito is an applied and computational harmonic analyst who is interested in feature extraction, graph signal processing, Laplacian eigenfunctions, and human and machine perception. He received the B.Eng. and the M.Eng. degrees in mathematical engineering from the University of Tokyo, Japan, in 1982 and 1984, respectively. Then, he received his Ph.D. degree in applied mathematics from Yale in 1994 while working at the Schlumberger Doll Research. In 1997, he joined the Department of Mathematics at the University of California, Davis, where he is currently a professor and a director of the UC Davis TETRAPODS Institute of Data Science (UCD4IDS), one of the NSF's Transdisciplinary Research In Principles Of Data Science (TRIPODS) Institutes that bring together the theoretical computer science, electrical engineering, mathematics, and statistics communities to develop the theoretical foundations of data science.

Dr. Saito received the Best Paper Awards from SPIE (1994) and JSIAM (2016) as well as the Henri Doll Award from Schl

Tue Nov 10

11:15am - Zoom
Climate Seminar
TBA
Mon Nov 09

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Nov 09

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Nov 09

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Nov 09

Math Biology Seminar

12:00pm - Via Zoom
Mechanics of Cell Packing in the Notochord
Sharon Lubkin, North Carolina State University
Abstract:

The notochord, the defining feature of chordates, is essentially a soft cylinder patterned in early development by a small number of interior cells. Our analysis of packing patterns of vacuolated cells in zebrafish notochords reveals that the characteristic "staircase" pattern, or the alternate patterns observed in mutants, are governed by a simple and robust geometric measure. We have also noted that the notochord is weakly elliptical in cross section. From these observations, and from similar observations in a model gel system, we have identified a bidirectional interaction between cell packing pattern and the cross section of the surrounding tube. We model the mechanics of the notochord tube three ways, identifying a second key nondimensional ratio governing the pattern formation, and revealing previously unobserved packing patterns.  Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Nov 09

Special Events and Seminars

11:00am - https://umn.zoom.us/j/92347592510
HA-GMT-PDE Seminar
Joseph Feneuil, Australian National University, Australia
Fri Nov 06

MCFAM Seminar

7:30pm - Zoom: https://umn.zoom.us/j/99433158383?pwd=T3h6
A Cluster Analysis Application Using only Social Determinant Variables to Predict Profiles of US Adults having the Highest Health Expenditures
Margie Rosenberg, University of Wisconsin - Madison
Abstract:

AttachedBio: Margie Rosenberg, PhD, FSA is the Assurant Health Professor of Actuarial Science Professor at the University of Wisconsin-Madison. Margies research interests are in the application of statistical methods to health care, and applying her actuarial expertise to cost and policy issues in health care. Her recent research involves linking social determinants to outcomes such as (i) assessing the impact of delayed attention to oral health issues on emergency department visits and (ii) assessing the impact of unhealthy behaviors on perceived health status and predicting individuals with persistent high expenditures. Prior to her starting on her academic career, Margie worked as a life actuary for Allstate Life Insurance Company in Northbrook, IL.Zoom Link: https://umn.zoom.us/j/99433158383?pwd=T3h6LzlTWCt4YW93Kzk3Rmg2bXQrZz09

Fri Nov 06

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Gröbner geometry of Schubert polynomials through ice
&nbsp;Anna Weigandt&nbsp;&nbsp;
Abstract:

The geometric naturality of Schubert polynomials and the related combinatorics of pipe dreams was established by Knutson and Miller (2005) via antidiagonal Gröbner degeneration of matrix Schubert varieties. We consider instead diagonal Gröbner degenerations. In this dual setting, Knutson, Miller, and Yong (2009) obtained alternative combinatorics for the class of vexillary matrix Schubert varieties. We will discuss general diagonal degenerations, relating them to an older formula of Lascoux (2002) in terms of the 6-vertex ice model.  Lascoux's formula was recently rediscovered by Lam, Lee, and Shimozono (2018), as "bumpless pipe dreams."  We will explain this connection and discuss conjectures and progress towards understanding diagonal Gröbner degenerations of matrix Schubert varieties.  This is joint work with Zachary Hamaker and Oliver Pechenik.  See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Nov 06

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Active Community Detection with Maximal Expected Model Change
Dan Kushnir, Nokia Bell Labs
Abstract:

We present a novel active learning algorithm for community detection on networks. Our proposed algorithm uses a Maximal Expected Model Change (MEMC) criterion for querying network nodes label assignments. MEMC detects nodes that maximally change the community assignment likelihood model following a query. Our work is inspired by detection in the benchmark Stochastic Block Model (SBM), where we provide  sample complexity analysis and empirical study with SBM and real network data for binary as well as for multi-class settings. We also cover the most challenging case of sparse degree and below-detection-threshold SBMs, where we observe a super-linear error reduction. MEMC is shown to be superior to the random selection baseline and other state-of-the-art active learners.

Dan Kushnir is a distinguished member of technical staff at Bell Laboratories Data Science group where he has been since 2012. Before that he held the Gibbs assistant professor position at Yale University's Applied Math Program from 2008 to 2012. He obtained his PhD at the Weizmann Institute of Science on the subject of Multiscale Tools for Data Analysis in 2008. He hold BsC in Computer Science from the Hebrew University in Jerusalem. His Current Interests Include Active Learning, efficient Sampling, Harmonic Analysis, Numerical Analysis and Randomized methods.

Fri Nov 06

10:10am - Zoom
MathCEP Seminar

Thu Nov 05

Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
Low-degree hardness of random optimization problems
David Gamarnik, Massachusetts Institute of Technology
Abstract:

We consider the problem of finding nearly optimal solutions of optimization problems with random objective functions. Two concrete problems we consider are (a) optimizing the Hamiltonian of a spherical or Ising p-spin glass model, and (b) finding a large independent set in a sparse Erdos-Renyi graph, both to be introduced in the talk. We consider the family of algorithms based on low-degree polynomials of the input. This is a general framework that captures methods such as approximate message passing and local algorithms on sparse graphs, among others. We show this class of algorithms cannot produce nearly optimal solutions with high probability. Our proof uses two ingredients. On the one hand both models exhibit the Overlap Gap Property (OGP) of near-optimal solutions. Specifically, for both models, every two solutions close to optimality are either close or far from each other. The second proof ingredient is the stability of the algorithms based on low-degree polynomials: a small perturbation of the input induces a small perturbation of the output. By an interpolation argument, such a stable algorithm cannot overcome the OGP barrier thus leading to the inapproximability. The stability property is established using concepts from Gaussian and Boolean Fourier analysis, including noise sensitivity, hypercontractivity, and total influence.

Joint work with Aukosh Jagannath and Alex Wein.

Thu Nov 05

11:15am - Zoom
Climate Seminar
TBA
Wed Nov 04

Probability Seminar

4:00pm - Via Zoom
Hypercontractivity, Convexity, and Lower Deviations
Petros Valettas, University of Missouri
Abstract:

The concentration of measure phenomenon is an indispensable tool in the study of high-dimensional phenomena.
Nonetheless, there exist several key situations that yields suboptimal results. We will discuss how this probabilistic principle admits stronger forms in the presence of convexity and how the local version of them can be combined with a blend of analytic, combinatorial, and topological methods in order to obtain sharp small ball probabilities for norms in high dimensions. Time permitting we will present applications in asymptotic geometric analysis. Based on joint work with Grigoris Paouris and Konstantin Tikhomirov.

Wed Nov 04

PDE Seminar

3:35pm - Via Zoom
The N-membrane problem
Hui Yu, Columbia University
Abstract:

The N-membrane problem is the study of shapes of elastic membranes being pushed against each other. The main questions are the
regularity of the functions modeling the membranes, and the regularity
of the contact regions between consecutive membranes.

These are classical questions in free boundary problems. However, very
little is known when N is larger than 2. In this case, there are
multiple free boundaries that cross each other, and most known
techniques fail to apply.

In this talk, we discuss, for general N, the optimal regularity of the
solutions in arbitrary dimensions, and a classification of blow-up
solutions in 2D. Then we focus on the regularity of the free
boundaries when N=3.

This talk is based on two recent joint works with Ovidiu Savin
(Columbia University).

Tue Nov 03

Dynamical Systems

2:30pm - Via Zoom
Dynamical Systems Seminar

Tue Nov 03

1:25pm - Zoom
Lecture
-, -
Tue Nov 03

IMA Data Science Lab Seminar

1:25pm - Online
Machine Learning Methods for Solving High-dimensional Mean-field Game Systems
Levon Nurbekyan, University of California, Los Angeles
Abstract:

Mean-field games (MFG) is a framework to model and analyze huge populations of interacting agents that play non-cooperative differential games with applications in crowd motion, economics, finance, etc. Additionally, the PDE that arise in MFG have a rich mathematical structure and include those that appear in optimal transportation and density flow problems. In this talk, I will discuss applications of machine-learning techniques to solve high-dimensional MFG systems. I will present Lagrangian, GAN-type, and kernel-based methods for suitable types of MFG systems.

I am currently an Assistant Adjunct Professor at the Department of Mathematics at UCLA. I previously held postdoctoral and visiting positions at McGill University, King Abdullah University of Science and Technology, National Academy of Sciences of Armenia, and the Technical University of Lisbon. I have also been a Senior Fellow at the Institute for Pure and Applied Mathematics (IPAM) at UCLA for its Spring 2020 Program on High Dimensional Hamilton-Jacobi PDEs and a Simons CRM Scholar at the University of Montreal for its Spring 2019 Program on Data Assimilation: Theory, Algorithms, and Applications.

Tue Nov 03

11:15am - Zoom
Climate Seminar
TBA
Mon Nov 02

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Nov 02

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Nov 02

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Nov 02

Math Biology Seminar

12:00pm - Zoom Details see abstract
Topological considerations in genome biology
Mariel Vazquez, University of California Davis
Abstract:

The genetic code of viruses and of living organisms is encoded in very long DNA or RNA molecules, which are tightly packaged in confined environments. Understanding the geometry and topology of nucleic acids is key to understanding the mechanisms of viral infection and the inner workings of a cell. We use techniques from knot theory and low-dimensional topology, aided by discrete methods and computational tools, to ask questions about the topological state of a genome. I will illustrate the use of these methods with examples drawn from our work on bacteriophages.Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Nov 02

Special Events and Seminars

11:00am - https://umn.zoom.us/j/92455367464
HA-GMT-PDE Seminar
Tomas Merchán Rodríguez, University of Minnesota, Minnesota
Fri Oct 30

MCFAM Seminar

7:30pm - Zoom: https://umn.zoom.us/j/99433158383?pwd=T3h6
Trends in applied mathematics and its adoption in the finance industry, or why you should pass on blockchains and big data
John Dodson, Options Clearing Corporation&nbsp;
Abstract:

Over the course of the twentieth century, applied mathematics has gradually assimilated and standardized the subjects of probability, statistics, control, and information. While an outside observer of decadal trends in STEM in finance might instead focus on the industry's embrace of computing technology during the Moore's Law era, I claim these quieter developments are ultimately more impactful because they help firms to organize information technology and financial innovation to create lasting value for clients. I will demonstrate this through a survey of the changing role of quants, and make an attempt to describe current opportunities.Bio: John is Vice President, Quantitative Risk Management at the Options Clearing Corporation in Chicago, which is the principal central counterparty for equity derivatives. Previously, John was with the treasury and investment risk management departments of Ameriprise Financial in Minneapolis. Prior to returning to the midwest, John worked for several major international banks in New York, London, and Zurich. He entered the industry out of college with an appointment at the Bank for International Settlements.

John is an Adjunct professor with MCFAMs Master of Financial Mathematics (MFM) program. In addition to his affiliation with MCFAMs MFM program, John has taught about financial derivatives for the Carlson School of Management and for various industry programs.

John has a BS degree in physics and mathematics from Stanford and an MS degree in computational finance from Carnegie Mellon. John's affiliation with the U of M goes back to the 80's. He was an UMTYMP student and also participated in a mentorship program with the head of the physics department during his high school years.

Fri Oct 30

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
The closed support problem over a complete intersection ring
Monica Lewis, University of Michigan
Abstract:

Local cohomology modules are (typically) very large algebraic objects that encode rich geometric information about the structure of a commutative ring. These modules are rarely finitely generated, but when the underlying space is smooth, there is often additional structure available that can lead to remarkable finiteness properties. For example, there are large classes of regular rings whose local cohomology is known to always have a finite set of associated primes. This property can fail over a complete intersection rings, but independent results of Hochster and Núñez-Betancourt (2017) or Katzman and Zhang (2017) have shown that at least in characteristic p > 0, the local cohomology of a hypersurface ring will still have closed support in the Zariski topology. It remains an open question whether this property holds in arbitrary codimension. In this talk, I will present my results on the local cohomology of a parameter ideal illustrating an obstruction to straightforwardly generalizing existing hypersurface strategies. I will then present joint work with Eric Canton on an alternative route of attack in higher codimension, involving a novel Frobenius-compatible simplicial complex of local cohomology modules.  See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Oct 30

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Estimating the Impact of Travel, Rest, and Playing at Home in the National Football League
Tom Bliss, National Football League (NFL)
Abstract:

Estimating schedule difficulty in the National Football League is tricky given the limited number of games and the number of factors that impact game outcomes, including time-varying team strengths, the home advantage, and changes in rest, travel, and time zones. From the league’s perspective, understanding each of these factors can give us a better understanding of scheduling equity and competitive balance. We extend the Bayesian state-space model of Lopez, Matthews, and Baumer (2018) to estimate varying levels of rest and travel advantages using betting market data. The model accounts for team strength that varies by week and season. We estimate that a team coming off a bye is worth about three-quarters of a point, while a shorter rest advantage is worth about half of that. In addition, we find that the benefit of playing at home has dropped approximately a point in the last decade and explore if and how the game looks different on the field as a result.

Thompson Bliss is a Data Scientist for the National Football League. He completed his master’s degree in Data Science at Columbia University in the City of New York in December 2019. At Columbia, he worked as a graduate assistant for a Sports Analytics course taught by Professor Mark Broadie. He received a Bachelor of Science in Physics and Astronomy at University of Wisconsin - Madison in 2018.

Fri Oct 30

10:10am - Zoom
MathCEP Seminar

Thu Oct 29

Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
The Weyl group and the nilpotent orbits
Zhiwei Yun, Massachusetts Institute of Technology
Abstract:

The Weyl group and the nilpotent orbits are two basic objects attached to a semisimple Lie group. The interplay between the two is a key ingredient in the classification of irreducible representations in various contexts. In this talk, I will describe two different constructions to relate these two objects due to Kazhdan-Lusztig, Lusztig and myself. I will concentrate on the construction using the loop geometry of the group. The main result is that the two seemingly different give the same maps between conjugacy classes in the Weyl group and the set of nipotent orbits.

Thu Oct 29

11:15am - Zoom
Climate Seminar
TBA
Wed Oct 28

Probability Seminar

4:00pm - Via Zoom
Random walks on dynamic random environments with non-uniform mixing
Marcelo Hilário, The Federal University of Minas Gerais
Abstract:

In this talk, we will discuss recent results on the limiting behavior of random walks on dynamic random environments. We will mainly discuss the case when then random walk evolves on one-dimensional random environments given by conservative interacting particle systems such as the simple symmetric exclusion process. Our results depend a great deal on space-time mixing properties imposed on the underlying environment and also on other features like the dimension and the type of allowed transitions. Conservation of particles leads to poor-mixing conditions which complicate the applicability of available tools and to overcome this difficulty we use renormalization to obtain the law of large numbers, large deviation estimates, and sometimes central limit theorems. The talk is based on several joint works with Oriane Blondel, Frank den Hollander, Daniel Kious, Renato dos Santos, and Vladas Sidoravicius.

Wed Oct 28

PDE Seminar

3:35pm - Via Zoom
Stationary Euler flows near the Kolmogorov and Poiseuille flows
Michele Coti Zelati, Imperial College London
Abstract:

We exhibit a large family of new, non-trivial stationary states of analytic regularity, that are arbitrarily close to the Kolmogorov flow on the square torus. Our construction of these stationary states builds on a degeneracy in the global structure of the Kolmogorov flow. This is in contrast with both the Kolmogorov flow on a rectangular torus and the Poiseuille flow in a channel, for which we can show that the only stationary states near them must be shears. This has surprising consequences in the context of inviscid damping in 2D Euler and enhanced dissipation in Navier-Stokes.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Tue Oct 27

Dynamical Systems

2:30pm - Via Zoom Link - see abstract
Dynamics on networks (and other things!)
Lee DeVille, University of Illinois
Abstract:

We will introduce several models connected to applications and present several results, mostly analytic but also some numerical.  These models will be defined on networks or higher-order objects (e.g. simplicial complexes).  In many of the cases, the dynamical systems can be characterized as nonlinear Laplacians; as such, various classical and not-so-classical results about Laplacians will be the secret sauce that undergirds the results.   We will also try to give some insight into the applications that give rise to the problems, as time permits.

Tue Oct 27

IMA Data Science Lab Seminar

1:25pm - Zoom
Clustering High-dimensional Data with Path Metrics: A Balance of Density and Geometry
Anna Little, The University of Utah
Abstract:

This talk discusses multiple methods for clustering high-dimensional data, and explores the delicate balance between utilizing data density and data geometry. I will first present path-based spectral clustering, a novel approach which combines a density-based metric with graph-based clustering. This density-based path metric allows for fast algorithms and strong theoretical guarantees when clusters concentrate around low-dimensional sets. However, the method suffers from a loss of geometric information, information which is preserved by simple linear dimension reduction methods such as classic multidimensional scaling (CMDS). The second part of the talk will explore when CMDS followed by a simple clustering algorithm can exactly recover all cluster labels with high probability. However, scaling conditions become increasingly restrictive as the ambient dimension increases, and the method will fail for irregularly shaped clusters. Finally, I will discuss how a more general family of path metrics, combined with MDS, give low-dimensional embeddings which respect both data density and data geometry. This new method exhibits promising performance on single cell RNA sequence data and can be computed efficiently by restriction to a sparse graph.

Anna Little received her PhD from Duke University in 2011, where she worked under Mauro Maggioni to develop a new multiscale method for estimating the intrinsic dimension of a data set. From 2012-2017 she was an Assistant Professor of Mathematics at Jacksonville University, a primarily undergraduate liberal arts institution where in addition to teaching and research she served as a statistical consultant. In 2018 she began a research postdoc in the Department of Computational Mathematics, Science, and Engineering at Michigan State University, where she worked with Yuying Xie and Matthew Hirn on statistical and geometric analysis of high-dimensional data. She recently accepted a tenure-track position in the Department of Mathematics at the University of Utah, which will begin in January 2021.

Tue Oct 27

11:15am - Zoom
Climate Seminar
TBA
Mon Oct 26

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 26

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Oct 26

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Oct 26

Math Biology Seminar

12:00pm - Zoom Details see abstract
A mathematical model for the Ion-dependent DNA Configuration in Bacteriophage Capsids
Pei Liu, University of Minnesota&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbs
Abstract:

Bacteriophages densely pack their long dsDNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystal structure, and experimental results have confirmed that it depends on the environmental ionic conditions. We propose a mathematical model to describe the dependence of DNA configurations inside bacteriophage capsids on different ion types and concentrations. The total free energy of the system combines the liquid crystal free energy, the electrostatic energy and the Lennard--Jones energy.  This energy determines the DNA and ionic distributions and is governed by a nonlinear second order partial differential equation (PDE).  The numerical results show good agreement with existing experiments and molecular dynamics simulations. In this talk, I will first briefly introduce the basic ideas in the liquid crystal theory and the electrolyte theory, then describe how we apply these ideas to model the DNA configuration in a bacteriophage capsid.

Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Oct 26

Special Events and Seminars

11:00am - https://umn.zoom.us/j/91393860723
HA-GMT-PDE Seminar
Alex Barron, University of Illinois - Urbana Champaign, Illinois
Fri Oct 23

MCFAM Seminar

Quantifying the Impact of the Social Determinants of Health in the Covid-19 Era
Shae Armstrong, Optum
Abstract:

The Social Determinants of Health (SDoH) are key factors in each persons environment and life that influence clinical outcomes of their health and wellbeing. These factors include, but are not limited to, income, housing, food security, education, and geography. In the age of Covid-19, understanding these factors and how they correlate to each other is more important than ever. Once we as industry gain insight on these clinical and financial impacts, we need to translate that insight into policy to mitigate root cause issues to better serve patients across the country. During this lecture we lay the foundation by defining what the Social Determinants of Health are and the various categories they fall into. We will also examine what data sources feed various SDoH models and limitations of said data sources. Next we will conduct a deep-dive examination on a variety of case studies and models aimed at quantifying the short-term and long-term clinical and financial impact of Covid-19. From there we will touch on the future and impact of healthcare data analytics within the healthcare industry and as human beings navigating an unprecedented pandemic.

Bio: Shae Armstrong is a Senior Healthcare Economic Consultant at OptumCare, a subsidiary of Optum, focusing on data strategy efforts to support a myriad of users from actuaries to data scientists who in turn, use data results to help providers make the best decisions for their patients. OptumCare is one of the largest healthcare systems in the nation, delivering care to patients in 15 states across the country. OptumCare is recognized nationally for its unique emphasis on data driven results and value-based care, creating a more effective and efficient kind of care. Data strategy efforts Shae currently supports ranges from data validation, standardization, and curation to defining data quality standards to operationalizing and optimizing data engines, streams, and processes. Prior to working at OptumCare, Shae was an Actuarial Analyst at Mercer Consulting working on actuarial pricing for a variety of state Medicaid programs. At Mercer she learned some of the fundamental data components and validations needed to support a wide variety actuarial and data science reporting needs. Shae is an alumnus of the University of Minnesota: Twin Cities where she double majored in Mathematics specializing in Actuarial Science (B.A.) and Economics (B.S.) with a minor in Risk Management and

Fri Oct 23

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Posets, Cones, and Toric Varieties
John Machacek, (from Hampden-Sydney College)
Abstract:

To any poset on [n] we can associate a cone in a natural way. This is done by a correspondence between i < j and the half-space x_i <= x_j. To any cone (or fan of cones) we have a toric variety. We consider translations back and forth between properties of posets and toric varieties. From this point of view we can establish Oda's strong factorization conjecture in the special case of fans arising from posets. We will also preview in progress work joint with Josh Hallam on crepant resolutions and the Gorenstein property for toric varieties associated to posets.

Fri Oct 23

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Lecture
Chris Finlay, Deep Render
Fri Oct 23

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
An Introduction to Image Compression, Old and New
Chris Finlay, Deep Render
Abstract:

Image compression, as a subset of image processing, intersects many areas of applied mathematics. In this talk, I will describe and compare the "classic" view of image compression, such as the JPEG algorithm and it's variants, against the "new kid on the block", namely compression using neural networks (NN). I will survey the relative merits of NN-based compression algorithms, provide a run-down of the inner workings, and discuss some of their flaws. We'll see that the neural network approach promises impressive performance gains over traditional image compression algorithms, though some hurdles still remain.

Chris Finlay is a research scientist at Deep Render, a UK startup focused on AI-based image and video compression. His background is in applied mathematics, but has spent time dabbling in machine leaning and computer science. Prior to moving to industry, he worked as a post-doc in machine learning, mainly researching neural ODEs, generative modeling, and the robustness of deep learning computer vision algorithms. He obtained a PhD in applied mathematics from McGill University, where he studied numerical methods for nonlinear elliptic PDEs.

Fri Oct 23

MathCEP Seminar

10:10am - Zoom
Evaluating process skills
Abstract:

ELIPSS (Enhanced Learning by Improving Process Skills in STEM) focuses on the identification, development, and assessment of process skills in active learning, undergraduate STEM classrooms. We will define several process skills and give rubrics to measure them.Zoom URL: https://umn.zoom.us/j/94699262069?pwd=ay9hbmU4V0pOWUFZZU5FTWZJMWFwdz09Zoom ID: 946 9926 206Zoom password: 7mwvv2

Thu Oct 22

Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
An analytic version of the Langlands correspondence for complex curves
Edward Frenkel, University of California, Berkeley
Abstract:

The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, Robert Langlands asked whether it is possible to construct a function-theoretic version. Together with Pavel Etingof and David Kazhdan, we have formulated a function-theoretic version as a spectral problem for (a self-adjoint extension of) an algebra of commuting differential operators on the moduli space of G-bundles of a complex algebraic curve.

I will start the talk with a brief introduction to the Langlands correspondence. I will discuss both the geometric and the function-theoretic versions for complex curves, and the relations between them. I will then present some of the results and conjectures from my joint work with Etingof and Kazhdan.

Thu Oct 22

11:15am - Zoom
Climate Seminar
TBA
Wed Oct 21

Probability Seminar

4:00pm - Via Zoom
On microscopic derivation of a continuum mean-curvature flow
Sunder Sethuraman, University of Arizona
Abstract:

We derive a continuum mean-curvature flow as a scaling limit of a class of zero-range + Glauber interacting particle systems. The zero-range part moves particles while preserving particle numbers, and the Glauber part allows birth and death of particles, while favoring two levels of particle density. When the two parts are simultaneously seen in certain (different) time-scales, and the Glauber part is bi-stable', a mean-curvature interface flow, incorporating a homogenized surface tension' reflecting microscopic rates, between the two levels of particle density, can be captured as a limit of the mass empirical density. This is work with Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst, and Hyunjoon Park.

Wed Oct 21

PDE Seminar

3:35pm - Via Zoom
Quantitative stability for minimizing Yamabe metrics
Robin Neumeyer, Northwestern University
Abstract:

The Yamabe problem asks whether, given a closed Riemannian manifold, one can find a conformal metric of constant scalar curvature (CSC). An affirmative answer was given by Schoen in 1984, following contributions from Yamabe, Trudinger, and Aubin, by establishing the existence of a function that minimizes the so-called Yamabe energy functional; the minimizing function corresponds to the conformal factor of the CSC metric.

We address the quantitative stability of minimizing Yamabe metrics. On any closed Riemannian manifold we showin a quantitative sensethat if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close to a CSC metric. Generically, this closeness is controlled quadratically by the Yamabe energy deficit. However, we construct an example demonstrating that this quadratic estimate is false in the general. This is joint work with Max Engelstein and Luca Spolaor.

Tue Oct 20

IMA Data Science Lab Seminar

1:25pm - Zoom
How COVID-19 has Changed the World and What the Future Holds
Michael Osterholm, University of Minnesota, Twin Cities
Abstract:

This presentation will provide a current and in depth review of the Covid-19 pandemic. It will also provide a glimpse into the future as to how this pandemic will continue to unfold and the impact it will have worldwide.

Dr. Osterholm is Regents Professor, McKnight Presidential Endowed Chair in Public Health, the director of the Center for Infectious Disease Research and Policy (CIDRAP), Distinguished Teaching Professor in the Division of Environmental Health Sciences, School of Public Health, a professor in the Technological Leadership Institute, College of Science and Engineering, and an adjunct professor in the Medical School, all at the University of Minnesota. From June 2018 through May 2019, he served as a Science Envoy for Health Security on behalf of the US Department of State. He is also on the Board of Regents at Luther College in Decorah, Iowa.

Tue Oct 20

11:15am - Zoom
Climate Seminar
TBA
Tue Oct 20

Dynamical Systems

10:00am - Zoom Link - See Abstract
Nonlinear stability of fast invading fronts in a Ginzburg-Landau equation with an additional conservation law
&nbsp;Bastian Hilder&nbsp;, University of Stuttgart&nbsp;&nbsp;
Abstract:

In this talk, I consider the stability of traveling fronts connecting an invading state to an unstable ground state in a Ginzburg-Landau equation with an additional conservation law. This system appears generically as an amplitude equation for Turing pattern forming systems admitting a conservation law structure such as the Bénard-Marangoni convection problem. The main result is the nonlinear stability of sufficiently fast fronts with respect to perturbations which are exponentially localized ahead of the front. The proof is based on the use of exponential weights ahead of the front to stabilize the ground state. After presenting the general strategy, I discuss the specific challenges faced in the proof, namely the lack of a comparison principle and the fact that the invading state is only diffusively stable, i.e. perturbations of the invading state decay polynomially in time.

Mon Oct 19

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 19

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Oct 19

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Oct 19

Math Biology Seminar

12:00pm - Via Zoom
Mathematical Virology: Geometry as a key to the discovery of novel anti-viral solutions
Reidun Twarock, University of York, UK&nbsp;
Abstract:

Viruses encapsulate their genetic material into protein containers that act akin to molecular Trojan horses, protecting viral genomes between rounds of infection and facilitating their release into the host cell environment. In the majority of viruses, including major human pathogens, these containers have icosahedral symmetry. Mathematical techniques from group, graph and tiling theory can therefore be used to better understand how viruses form, evolve and infect their hosts, and point the way to novel antiviral solutions. In this talk, I will present a theory of virus architecture, that contains the seminal Caspar Klug theory as a special case and solves long-standing open problems in structural virology. I will also introduce mathematical models of symmetry breaking in viral capsids and discuss their consequences for our understanding of more complex viral geometries. By combining these geometric insights with a range of different mathematical and computational modelling techniques, I will demonstrate how viral life cycles can be better understood through the lens of viral geometry, and how such insights can act as drivers of discovery of novel anti-viral solutions. Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Mon Oct 19

Special Events and Seminars

11:00am - https://umn.zoom.us/j/97066564629
HA-GMT-PDE Seminar
Dallas Albritton, Courant Institute, New York
Fri Oct 16

MCFAM Seminar

Multi-Step Forecast of Implied Volatility Surface using Deep Learning
Zhiguang (Gerald) Wang, South Dakota State University&nbsp;
Abstract:

Modeling implied volatility surface (IVS) is of paramount importance to price and hedge an option. We contribute to the literature by modeling the entire IVS using recurrent neural network architectures, namely Convolutional Long Short Term Memory Neural Network (ConvLSTM) to produce multivariate and multi-step forecasts of the S&P 500 implied volatility surface. Using the daily S&P 500 index options from 2002 to 2019, we benchmark the ConvLSTM model against traditional multivariate time series VAR model, VEC model, and LSTM neural network. We find that both LSTM and ConvLSTM can fit the training data extremely well with mean absolute percentage error (MAPE) being 3.56%  and 3.88%, respectively. As for out-of-sample data, the ConvLSTM (8.26% ) model significantly outperforms traditional time series models as well as the LSTM model for a 1-day, 30-day, and 90-day horizon, for all moneyness groups and contract months of both calls and puts.  Zoom Link: https://umn.zoom.us/j/99433158383?pwd=T3h6LzlTWCt4YW93Kzk3Rmg2bXQrZz09

Fri Oct 16

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Polarizations of Powers of Graded Maximal Ideals
Ayah Almousa, Cornell University
Abstract:

Given a monomial ideal, one can "polarize" it to a square-free monomial ideal that has all of the same homological invariants as the original one. Many commutative algebraists are familiar with the use of the "standard" polarization, but the first major use of a nonstandard polarization was by Uwe Nagel and Vic Reiner in the early 2000s, who used the "box polarization" to produce a minimal cellular resolution for strongly stable ideals. This leads to the natural question: what other ways are there to polarize a monomial ideal, and what other applications might there be for these non-standard polarizations? In this talk, I will give a complete combinatorial characterization of all possible polarizations of powers of the graded maximal ideal in a polynomial ring. I will also give a combinatorial description of their Alexander duals and discuss applications of polarizations to commutative algebra, algebraic geometry, and combinatorics. This is joint work with Gunnar Fløystad and Henning Lohne. See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Oct 16

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Systems Modeling in Biopharma
Helen Moore, Applied BioMath
Abstract:

Quantitative systems pharmacology (QSP) models are increasingly being used for decision making in the biotechnology/pharmaceutical (biopharma) industry. QSP models are typically systems of ordinary differential equations with some mechanistic level of detail of the disease and a therapy. Parameters in a QSP model may be estimated from data, or obtained from the literature or from input from disease/biology experts. Once parameter values or distributions are determined, a QSP model can be used for predictive purposes. I will show some examples of QSP models used in projects for various applications in the biopharma industry. I will also mention some of the issues and open problems for the use of QSP models.

Dr. Moore is a mathematician who spent 11 years in academia working in modeling and optimization, primarily in oncology, immunology, and virology. While in academia, she won two teaching awards and received a National Science Foundation grant for her research. During 14 years in the biopharma industry, she has worked in a variety of therapeutic areas and drug development stages at Genentech, Certara, Bristol-Myers Squibb, AstraZeneca, and now Applied BioMath. In 2018, she was named a Fellow of the Society for Industrial and Applied Mathematics. Her current work includes mechanistic ODE systems modeling, modeling of tumor dynamics, optimization of combination regimens, and quantitative evaluation of predictive mathematical models. She graduated from the University of North Carolina at Chapel Hill in 1989, and earned her PhD in mathematics from Stony Brook University in New York in 1995.

Thu Oct 15

Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
The diffeomorphism group of a 4-manifold
Daniel Ruberman, Brandeis University
Abstract:

Associated to a smooth n-dimensional manifold are two infinite-dimensional groups: the group of homeomorphisms Homeo(M), and the group of diffeomorphisms, Diff(M). For manifolds of dimension greater than 4, the topology of these groups has been intensively studied since the 1950s. For instance, Milnor's discovery of exotic 7-spheres immediately shows that there are distinct path components of the diffeomorphism group of the 6-sphere that are connected in its homeomorphism group. The lowest dimension for such classical phenomena is 5.

I will discuss recent joint work with Dave Auckly about these groups in dimension 4. For each n, we construct a simply connected 4-manifold Z and an infinite subgroup of the nth homotopy group of Diff(Z) that lies in the kernel of the natural map to the corresponding homotopy group of Homeo(Z). These elements are detected by (n+1)-parameter gauge theory. The construction uses a topological technique.

Thu Oct 15

11:15am - Zoom
Climate Seminar
TBA
Wed Oct 14

Probability Seminar

4:00pm - Via Zoom
NU-UMN Joint Probability Seminar

Wed Oct 14

PDE Seminar

3:35pm - Via Zoom
Lisa Naples, Macalaster College
Abstract:

In geometric measure theory there is interest in understanding measures by studying interactions with particular collections of sets. Here, we will discuss a recent characterization of Radon measures on R^n which are carried by the collection of m-Lipschitz graphs. That is, we will provide necessary and sufficient conditions for a Radon measure under which there exist countably many Lipschitz graphs that capture almost all of the mass. Our characterization will involve only countably many evaluations of the measure. This is joint work with Matthew Badger.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Tue Oct 13

Dynamical Systems

2:30pm - Zoom link: See abstract
A coordinate transformation to highlight interesting flow features: local orthogonal rectification
Jonathan Rubin, University of Pittsburgh
Abstract:

Following some pioneering earlier work, there has been an uptick in efforts to develop coordinate transformations that provide natural coordinate systems in which it becomes easier to study certain flow features. Many of these transformations are local or focus on periodic orbits and associated small perturbations. In this talk, I will introduce a new coordinate transformation, local orthogonal rectification (LOR), recently developed by my graduate student Ben Letson (SFL Scientific) and me. I will illustrate how LOR provides new insights about forms of transient dynamics including rivers, dynamics of trajectories as they approach periodic orbits, and canards, and represents a useful tool that others may wish to apply for the analysis of such phenomena.

Tue Oct 13

IMA Data Science Lab Seminar

1:25pm - Zoom
Geometric Methods in Statistics, Optimization, and Sampling
Tyler Maunu, Massachusetts Institute of Technology
Abstract:

I will address some recent developments in geometric methods for optimization, statistics, and sampling. Within three specific examples, I will demonstrate how one can leverage geometric structure to achieve: 1) robust recovery results for nonconvex estimators, 2) fast statistical rates in Wasserstein barycenter estimation, and 3) efficient sampling algorithms. First, in regard to robust recovery, I consider the problems of robust subspace recovery and robust synchronization. Each of these problems has an underlying manifold structure that is exploited to yield state-of-the-art robustness guarantees and efficient algorithms. Next, I will discuss the problem of statistical estimation of Wasserstein barycenters and develop a condition that ensures fast rates for an efficiently computable estimator. Finally, I will show how the leveraging the structure of gradient flows on Wasserstein space allows one to develop fast rates of convergence for sampling algorithms. The discretization of these flows leads to novel sampling algorithms that offer distinct advantages over existing methods.

Tyler received his Ph.D. in Mathematics and M.S. in Statistics from the University of Minnesota in 2018, where he worked with Prof. Gilad Lerman on the problem of robust subspace recovery. Since then, he has been an Instructor in Applied Mathematics at MIT, where he has worked with Prof. Philippe Rigollet on problems related to optimization, optimal transport, and sampling.

Tue Oct 13

11:15am - Zoom
Climate Seminar
TBA
Mon Oct 12

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 12

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Oct 12

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Fri Oct 09

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Combinatorics and CoEulerian Representations for Coincidental Reflection Groupsmmutative Algebra
Sarah Brauner, University of Minnesota
Abstract:

The Eulerian idempotents of a real reflection group and the representations they generate are a topic of longstanding interest to combinatorialists, representation theorists and topologists. In Type A, these representations have connections to the braid arrangement, Solomon's descent algebra, and mysteriously arise as the graded pieces of the cohomology of the configuration space of $n$ ordered points in $\mathbb{R}^3$. In this talk, I will describe how this relationship generalizes to real reflection groups of coincidental type---that is, reflection groups whose exponents form an arithmetic progression---by characterizing the Eulerian representations as (among other things) components of the associated graded Varchenko-Gelfand ring. All of the above concepts will be defined during the talk. See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Thu Oct 08

MCFAM Distinguished Lecture Series

5:30pm - Via Zoom
Climate Change and Insurance
Vijay Manghanani, SVP, Risk &amp; Analytics, PIMCO ILS Fund, Chief Risk Officer/Chief Actuarial Officer at Newport Re
Abstract:

Climate Change is one of the most significant and yet poorly understood risks faced by organizations today. While there is general consensus on the climate impact of continued greenhouse gas emissions, there remains significant uncertainty in the exact timing and severity of most serious extreme events. This uncertainty has led to a 'tragedy of the horizons' among much of the financial sector, where short term risks and financial decisions need to be balanced against long term secular risks introduced by climate change. The risks posed by climate change can be broadly classified into two categories, physical and transition risks. Physical risks refer to the increased direct exposure to changing frequency and severity of extreme events. Transition risks pertain to impacts on traditional business models and sectors as society shifts towards a lower carbon economy. A comprehensive analysis for these risks necessarily involves rigorous portfolio stress testing and scenario analysis on both the asset and liability side of the balance sheet. While climate change is a global phenomenon, the specific weather extremes are very local. The embedded correlations and non-linear impacts  make financial outcome distributions skewed and fat tailed. The financial models used to assess climate change risk need to adequately reflect the complex spatio-temporal interactions between nature and physical/financial assets. The insurance industry, in its key role as a risk transfer intermediary is often at the forefront of the financial impacts of climate change. The industry is not a novice to dealing with climate risks emanating from extreme events, such as hurricanes, floods, wildfires, etc. In response to the significant earnings and capital impacts of such extreme events, the industry has evolved over the past 3 decades, a fairly robust toolkit to assess physical climate risks using sophisticated catastrophe risk models. We will discuss how these models can help assess physical climate risks in insurance portfolios and how a similar approach might be adapted for broader finance portfolios.  Bio: Dr. Manghnani is a senior risk and analytics executive at the PIMCO with a focus on the Insurance Linked Security asset class. He is also the Chief Actuary and Chief Risk Officer at Newport Re. Most recently, he was the Head of Catastrophe Risk Management and Analytics COE at AIG. In this role, he was responsible for implementing state of the art

Thu Oct 08

Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
Mean-field disordered systems and Hamilton-Jacobi equations
Jean-Christophe Mourrat, Courant Institute of Mathematical Sciences, New York University
Abstract:

The goal of statistical mechanics is to describe the large-scale behavior of collections of simple elements, often called spins, that interact through locally simple rules and are influenced by some amount of noise. A celebrated model in this class is the Ising model, where spins can take the values +1 and -1, and the local interaction favors the alignement of the spins.

In this talk, I will mostly focus on the situation where the interactions are themselves disordered, with some pairs having a preference for alignement, and some for anti-alignement. These models, often called "spin glasses", are already surprisingly difficult to analyze when all spins directly interact with each other. I will describe a fundamental result of the theory called the Parisi formula. I will then explain how this result can be recast using suitable Hamilton-Jacobi equations, and what benefits this new point of view may bring to the topic.

Thu Oct 08

11:15am - Zoom
Climate Seminar
TBA
Wed Oct 07

Probability Seminar

4:00pm - Via Zoom
The r-to-p norm of non-negative random matrices
Souvik Dhara, MIT
Abstract:

For an n\times n matrix A_n, the r\to p operator norm is defined as \|A_n\|_{r\to p}:= \sup_{x \in R^n:\|x\|_r\leq 1 } \|A_n\|_p for r, p\geq 1. For different choices of r and p, this norm corresponds to key quantities that arise in diverse applications including matrix condition number estimation, clustering of data, and finding oblivious routing schemes in transportation networks. This talk considers r\to p norms of symmetric random matrices with nonnegative entries, including adjacency matrices of  Erdos-Renyi random graphs, matrices with positive sub-Gaussian entries, and certain sparse matrices. For 1< p\leq r< \infty, the asymptotic normality,  as n\to\infty, of the appropriately centered and scaled norm \|A_n\|_{r\to p} is established. Furthermore,  a sharp \ell_\infty-approximation for the unique maximizing vector in the definition of \|A_n\|_{r\to p} is obtained, which may be of independent interest. In fact, the vector approximation result is shown to hold for a broad class of deterministic sequence of matrices having certain asymptotic expansion properties. The results obtained can be viewed as a  generalization of the seminal results of F\"{u}redi and  Koml\'{o}s (1981) on asymptotic normality of the largest singular value of a class of symmetric random matrices, which corresponds to the special case r=p=2 considered here. In the general case with 1< p\leq r < \infty, the spectral methods are no longer applicable, which requires a new approach, involving a refined convergence analysis of a nonlinear power method and establishing a perturbation bound on the maximizing vector.

This is based on a joint work with Debankur Mukherjee (Georgia Tech) and Kavita Ramanan (Brown University).

Wed Oct 07

PDE Seminar

3:35pm - Via Zoom
Two problems related to the boundary layer in fluids
Siming He, Duke University&nbsp;
Abstract:

In this talk, I will present two works related to boundary layers in thefluid. The first result concerns the 2D Navier-Stokes equations linearized around the Couette flow in the periodic channel in the vanishing viscosity limit. We split the vorticity evolution into thefree-evolution (without a boundary) and a boundary corrector that is exponentially localized. If the initial vorticity perturbation is supported away from the boundary, we show inviscid damping of both thevelocity and the boundary layer's vorticity. We also observe that both velocity and vorticity satisfy the expected enhanced dissipation. This is joint work with Jacob Bedrossian. The second work is related to aboundary layer model designed to understand the Hou-Luo Scenario associated with the 3D Euler equation's blow-up. We show that there exists initial data which yields blow-up in the model. This is joint workwith Alexander Kiselev.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Tue Oct 06

Dynamical Systems

2:30pm - Zoom link: See abstract
Epidemiological Forecasting with Simple Nonlinear Models
&nbsp;Joceline Lega&nbsp;, University of Arizona
Abstract:

Every week, the CDC posts COVID-19 death forecasts for the US and its states and territories. These estimates are created with an ensemble model that combines probabilistic predictions made by a variety of groups in the US and abroad. Our model, EpiCovDA, which is developed by mathematics graduate student Hannah Biegel and combines simple nonlinear modeling with data assimilation, is one of these contributions. In this talk, I will present a novel paradigm for epidemiological modeling that is based on a dynamical systems perspective, and which consists in describing an outbreak in terms of incidence versus cumulative case curves. I will then explain how this approach may be used for parameter estimation and how it is combined with data assimilation in EpiCovDA. Zoom Link: https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Oct 06

IMA Data Science Lab Seminar

1:25pm - Zoom
Large-Scale Semi-supervised Learning via Graph Structure Learning over High-dense Points
Li Wang, University of Texas at Arlington
Abstract:

We focus on developing a novel scalable graph-based semi-supervised learning (SSL) method for a small number of labeled data and a large amount of unlabeled data. Due to the lack of labeled data and the availability of large-scale unlabeled data, existing SSL methods usually encounter either suboptimal performance because of an improper graph or the high computational complexity of the large-scale optimization problem. In this paper, we propose to address both challenging problems by constructing a proper graph for graph-based SSL methods. Different from existing approaches, we simultaneously learn a small set of vertexes to characterize the high-dense regions of the input data and a graph to depict the relationships among these vertexes. A novel approach is then proposed to construct the graph of the input data from the learned graph of a small number of vertexes with some preferred properties. Without explicitly calculating the constructed graph of inputs, two transductive graph-based SSL approaches are presented with the computational complexity in linear with the number of input data. Extensive experiments on synthetic data and real datasets of varied sizes demonstrate that the proposed method is not only scalable for large-scale data, but also achieve good classification performance, especially for extremely small number of labels.

Dr. Li Wang is currently an assistant professor with Department of Mathematics and Department of Computer Science Engineering, University of Texas at Arlington, Texas, USA. She worked as a research assistant professor with Department of Mathematics, Statistics, and Computer Science at University of Illinois at Chicago, Chicago, USA from 2015 to 2017. She worked as the Postdoctoral Fellow at University of Victoria, BC, Canada in 2015 and Brown University, USA, in 2014. She received her Ph.D. degree in Department of Mathematics at University of California, San Diego, USA, in 2014. Her research interests include data science, large-scale optimization and machine learning.

Tue Oct 06

11:15am - Zoom
Climate Seminar
TBA
Mon Oct 05

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 05

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Oct 05

Student Number Theory Seminar

1:00pm - Via Zoom
Student Number Theory Seminar

Mon Oct 05

Special Events and Seminars

11:00am - https://umn.zoom.us/j/93698530123
HA-GMT-PDE Seminar
Hong Wang, Institute for Advanced Study, New Jersey
Fri Oct 02

MCFAM Seminar

7:30pm - Zoom : https://umn.zoom.us/j/99433158383?pwd=T3h
Efficient Risk-sensitivity Estimation for Equity-Linked Insurance Benefits
Liban Mohammed, University of Wisconsin -Madison
Abstract:

For an organization with billions of dollars in assets, precise risk management is necessary to safeguard those assets. However, when the risks these assets are exposed to depend on the future performance of equities in complex ways, directly estimating them in real-time to the necessary precision can be prohibitively expensive. This talk discusses some approaches to resolving this tension via metamodeling techniques.Bio: Liban Mohamed is a final-year PhD student in the UW-Madison Department of Mathematics. His research focuses on the scattering theory of solutions to the Schrodinger equation on discrete spaces. The content of this talk is the result of a project hosted by the 2020 IMA Math-to-Industry Boot Camp with industry partners at Securian Financial.Zoom Link: https://umn.zoom.us/j/99433158383?pwd=T3h6LzlTWCt4YW93Kzk3Rmg2bXQrZz09

Fri Oct 02

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Random Flag Complexes and Torsion in Syzygies of Random Monomial Ideals
Jay Yang, University of Minnesota
Abstract:

In our paper Random Flag Complexes and Asymptotic Syzygies, Daniel Erman and I constructed a model of a random monomial ideal, and showed that the Betti tables for the ideals in this model exhibited asymptotic behavior reminiscent of the Veronese module. This inspired recent work with Daniel Erman and Caitlyn Booms showing that Stanley--Reisner ideals corresponding to random flag complexes almost always have Betti tables that depend on characteristic. We use this to offer a heuristic on when to expect that the syzygies of the Veronese should depend on characteristic.See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Oct 02

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Combinatorial Algorithms for National Security
Cynthia Phillips, Sandia National Laboratories
Abstract:

Working at a national laboratory can be somewhere in between academia and industry. I will describe my perspective of what makes working at a lab unique, based on my experience in the Computing Research Center at Sandia National Laboratories. I will mention skills that will help a researcher succeed in this environment, many just those that will help anywhere. The constraints and priorities of national-security problems often give even abstracted problems unusual twists. I will summarize some example research projects from data science (streaming data management for cybersecurity, cooperative computing among autonomous data centers for counterterrorism) to solvers (highly parallel branch and bound) to the intersection of government and industry (e.g. sensor placement for municipal water networks with the US EPA).

Cynthia Phillips is a senior scientist at Sandia National Laboratories.  In her 30 years at the lab she has conducted research in combinatorial optimization, algorithm design and analysis, and parallel computation with more recent work in data science such as streaming algorithms. The applications reflect some of the diversity of Sandia's mission including scheduling, network and infrastructure surety, computational biology, computer security, quantum computing, neuromorphic computing, hardware/algorithm co-design, social network analysis, wireless networks and sensor placement (e.g. for municipal water networks for the EPA). Her work spans highly theoretical papers to general-purpose codes to applications. She has done extensive professional service including being a professional society officer and a conference chair. She is an Association for Computing Machinery distinguished scientist and a Society for Industrial and Applied Mathematics fellow. She received a B.A. in applied mathematics from Harvard University and a PhD in computer science from MIT.

Thu Oct 01

Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
Richard Kenyon, Yale University
Abstract:

This is joint work with Istvan Prause. Many well-known random tiling models such as domino tilings and square ice lead to variational problems for functions h:R^2->R which minimize a functional depending only on the gradient of h. Other examples of such variational problems include minimal surfaces and surfaces satisfying the "p-laplacian". We give a representation of solutions of such a problem in terms of kappa-harmonic functions: functions which are harmonic for a laplacian with a varying conductance kappa.

Thu Oct 01

11:15am - Zoom
Climate Seminar
TBA
Wed Sep 30

Probability Seminar

4:00pm - Via Zoom
Empirical measures, geodesic lengths, and a variational formula in first-passage percolation
Abstract:

We consider the standard first-passage percolation model on Z^d, in which each edge is assigned an i.i.d. nonnegative weight, and the passage time between any two points is the smallest total weight of a nearest-neighbor path between them.  Our primary interest is in the empirical measures of edge-weights observed along geodesics from 0 to ne_1.  For various dense families of edge-weight distributions, we prove that these measures converge weakly to a deterministic limit as n tends to infinity.  The key tool is a new variational formula for the time constant.  In this talk, I will derive this formula and discuss its implications for the convergence of both empirical measures and lengths of geodesics.

Wed Sep 30

PDE Seminar

3:35pm - https://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi
On the Cauchy problem for the Hall magnetohydrodynamics
Sungjin Oh, University of California Berkeley&nbsp;
Abstract:

In this talk, I will describe a recent series of work with I.-J. Jeong on the incompressible Hall MHD equation without resistivity. This PDE, first investigated by the applied mathematician M. J. Lighthill, is a one-fluid description of magnetized plasmas with a quadratic second-order correction term (Hall current term), which takes into account the motion of electrons relative to positive ions. Curiously, we demonstrate the ill(!)posedness of the Cauchy problem near the trivial solution, despite the apparent linear stability and conservation of energy. Our ill posedness mechanism is sharp, in that it remains true under fractional dissipation of any subcritical order. On the other hand, we identify several regimes in which the Cauchy problem is well-posed, which not only includes the original setting that M. J. Lighthill investigated (namely, for initial data close to a uniform magnetic field) but also possibly large perturbations thereof. Central to our proofs is the viewpoint that the Hall current term imparts the magnetic field equation with a quasilinear dispersive character. With such a viewpoint, the key ill- and well-posedness mechanisms can be understood in terms of the properties of the bi-characteristic flow associated with the appropriate principal symbol.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Tue Sep 29

Dynamical Systems

2:30pm - Via Zoom
Dynamical Systems Seminar

Tue Sep 29

IMA Data Science Lab Seminar

1:25pm - Online
Multi-Perspective, Simultaneous Embedding and Theoretically Guaranteed Projected Power Method for the Multi-way Matching Problem
Vahan Huroyan, University of Arizona
Abstract:

We address two important subproblems of Structure from Motion Problem. The first subproblem is known as Multi-way Matching, where the input includes multiple sets, with the same number of objects and noisy measurements of fixed one-to-one correspondence maps between the objects of each pair of sets. Given only noisy measurements of the mutual correspondences, the Multi-way Matching problem asks to recover the correspondence maps between pairs of them. The desired output includes the original fixed correspondence maps between all pairs of sets. The second subproblem is called Multi-Perspective Simultaneous Embedding (MPSE). The input for MPSE assumes a set of pairwise distance matrices defined on the same set of objects and possibly along with the same number of projection operators. MPSE embeds points in 3D so that the pairwise distances are preserved under the corresponding projections. Our proposed algorithm for Multi-way Matching problem iteratively solves the associated non-convex optimization problem. We prove that for a specific noise model, if the initial point of our proposed iterative algorithm is good enough, the algorithm linearly converges to the unique solution. Numerical experiments demonstrate that our method is much faster and more accurate than the state-of-the-art methods. For MPSE, we propose a heuristic algorithm and provide an extensive quantitative evaluation with datasets of different sizes, as well as several examples that illustrate the quality of the resulting solutions.

I received my PhD in mathematics from the University of Minnesota in 2018, under the supervision of my advisor Prof. Gilad Lerman. Since 2018, I've been working as a Postdoctoral Research Associate at the Department of Mathematics of the University of Arizona.

Tue Sep 29

11:15am - Zoom
Climate Seminar
TBA
Mon Sep 28

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 28

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Sep 28

Special Events and Seminars

11:00am - https://umn.zoom.us/j/96572145611
HA-GMT-PDE Seminar
Hyunwoo Kwon, Republic of Korea Air Force Academy, South Korea
Fri Sep 25

MCFAM Seminar

7:30pm - https://umn.zoom.us/j/99433158383?pwd=T3h6LzlTWC
Actuarial Implications of COVID-19
Max Rudolph, &nbsp;Rudolph Financial&nbsp;&nbsp;

Fri Sep 25

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
On a Rank-Unimodality Conjecture of Morier-Genoud and Ovsienko
Bruce Sagan, Michigan State University
Abstract:

Let $\alpha=(a,b,\ldots)$ be a composition. Consider the associated poset $F(\alpha)$, called a fence, whose covering relations are $$x_1\lhd x_2 \lhd \ldots\lhd x_{a+1}\rhd x_{a+2}\rhd \ldots\rhd x_{a+b+1}\lhd x_{a+b+2}\lhd \ldots\.$$ We study the associated distributive lattice $L(\alpha)$ consisting of all lower order ideals of $F(\alpha)$. These lattices are important in the theory of cluster algebras and their rank generating functions can be used to define $q$-analogues of rational numbers. In particular, we make progress on a recent conjecture of Morier-Genoud and Ovsienko that $L(\alpha)$ is rank unimodal. We show that if one of the parts of $\alpha$ is greater than the sum of the others, then the conjecture is true. We conjecture that $L(\alpha)$ enjoys the stronger properties of having a nested chain decomposition and having a rank sequence which is either top or bottom interlacing, the latter being a recently defined property of sequences. We verify that these properties hold for compositions with at most three parts and for what we call $d$-divided posets, generalizing work of Claussen and simplifying a construction of Gansner. This is joint work with Thomas McConville and Clifford Smyth.See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Sep 25

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
The Technical and Organizational Challenges of Data Science
Catherine (Katy) Micek, 3M
Abstract:

In October 2012 – shortly after I began my career in the data science space – the Harvard Business Review published the article “Data Scientist: The Sexiest Job of the 21st Century” and generated an enormous amount of buzz about the field. Since then, data science has matured: technical skill sets required to do the work are better defined and specializations are emerging. However, the field is still evolving and how data science is used by an organization can vary greatly. In such a dynamic and broadly defined field, it has been my experience that data scientists need to have a wide range of technical skills augmented by soft skills in order to be successful. In this talk, I will share my experience working as a predictive modeler, data scientist, and software developer across various industries (insurance, energy, and within 3M), as well as provide examples of challenges I’ve encountered as a data scientist. I will also discuss my work on a Digital Solutions Implementation for 3M’s Knoxville plant, a project where we are exploring how data science to understand and reduce product variability for Acrylic Foam Tape.

Catherine (Katy) Micek is a Data Scientist at 3M in St. Paul, Minnesota. She holds a Ph.D. in Applied Mathematics from the University of Minnesota. In her Ph.D. thesis, Katy developed mathematical models for polymer gel swelling with applications to artificial bone implants and drug-delivery devices. Katy has worked in both academic and industrial positions since earning her degree. In addition to teaching college mathematics, she has worked on crossfunctional business teams as a data scientist, software developer, and predictive modeler teams across diverse industries (insurance, energy, finance, supply chain, and manufacturing). Katy is also an active speaker and mentor. She is frequently invited to college, universities, and conferences to discuss her technical work and career experiences in data science, and she is a contributor to publications by the Society of Industrial and Applied Mathematics on industrial career options. In her free time, Katy enjoys spending time with friends and family, as well as ballroom dancing, rock climbing, and cooking.

Thu Sep 24

Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
Random walks in graph-based learning
Jeff Calder, University of Minnesota, Twin Cities
Abstract:

I will discuss several applications of random walks to graph-based learning, both for theoretical analysis and algorithm development. Graph-based learning is a field within machine learning that uses similarities between datapoints to create efficient representations of high-dimensional data for tasks like semi-supervised classification, clustering and dimension reduction. Our first application will be to use the random walk interpretation of the graph Laplacian to characterize the lowest label rate at which Laplacian regularized semi-supervised learning is well-posed. Second, we will show how analysis via random walks leads to a new algorithm that we call Poisson learning for semi-supervised learning at very low label rates. Finally, we will show how stochastic coupling of random walks can be used to prove Lipschitz estimates for graph Laplacian eigenfunctions on random geometric graphs, leading to new spectral convergence results.

This talk will cover joint work with many people, including Brendan Cook (UMN), Nicolas-Garcia Trillos (Wisconsin-Madison), Marta Lewicka (Pittsburgh), Dejan Slepcev (CMU), Matthew Thorpe (University Manchester).

Thu Sep 24

11:15am - Zoom
Climate Seminar
TBA
Thu Sep 24

Special Events and Seminars

11:00am - https://umn.zoom.us/j/93601442665
HA-GMT-PDE Seminar
Bingyang Hu, Purdue University, Indiana
Wed Sep 23

Probability Seminar

9:00am - Via Zoom
Forest fire processes and near-critical percolation with heavy-tailed impurities
Pierre Nolin, City University of Hong Kong
Abstract:

We discuss models of forest fires (or epidemics): on a given planar lattice, all vertices are initially vacant, and then become occupied at rate 1. If an occupied vertex is hit by lightning, which occurs at a (typically very small) rate, all the vertices connected to it "burn" instantaneously, i.e. they become vacant. We want to analyze the behavior of such processes near and beyond the critical time (the time after which, in the absence of fires, infinite connected components would emerge).

We are led to introduce a percolation model where regions ("impurities") are removed from the lattice, in an independent fashion. These impurities are not only microscopic, but also allowed to be mesoscopic. We are interested in whether the connectivity properties of percolation remain of the same order as without impurities, for values of the percolation parameter close to the critical value. This generalizes a celebrated result by Kesten for near-critical percolation (that can be viewed as critical percolation with single-site impurities).

This talk is based on a joint work with Rob van den Berg (CWI and VU, Amsterdam).

Tue Sep 22

Dynamical Systems

2:30pm - Zoom - see link below
Anderson localization for disordered trees
Selim Sukhtaiev, Auburn University
Abstract:

In this talk, we will discuss a mathematical treatment of a disordered system modeling localization of quantum waves in random media. We will show that the transport properties of several natural Hamiltonians on metric and discrete trees with random branching numbers are suppressed by disorder. This phenomenon is called Anderson localization.

https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Sep 22

IMA Data Science Lab Seminar

1:25pm - Online
Matrix Denoising with Weighted Loss
William Leeb, University of Minnesota, Twin Cities
Abstract:

This talk will describe a new class of methods for estimating a low-rank matrix from a noisy observed matrix, where the error is measured by a type of weighted loss function. Such loss functions arise naturally in a variety of problems, such as submatrix denoising, filtering heteroscedastic noise, and estimation with missing data. We introduce a family of spectral denoisers, which preserve the left and right singular subspaces of the observed matrix. Using new asymptotic results on the spiked covariance model in high dimensions, we derive the optimal spectral denoiser for weighted loss. We demonstrate the behavior of our method through numerical simulations.

William Leeb is an Assistant Professor in the School of Mathematics at the University of Minnesota, Twin Cities. He earned his PhD from Yale University in 2015 under the supervision of Ronald Coifman, and from 2015 to 2018 was a postdoc in Amit Singer's research group at Princeton University. William's research is in applied and computational harmonic analysis, statistical signal processing, and machine learning. He is particularly interested in estimation problems with low signal-to-noise ratios, high dimensionality, and many nuisance parameters.

Tue Sep 22

11:15am - Zoom
Climate Seminar
TBA
Mon Sep 21

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 21

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Sep 18

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Betti numbers of unordered configuration spaces of a punctured torus
Yifeng Huang, University of Michigan
Abstract:

Let X be a elliptic curve over C with one point removed, and consider the unordered configuration spaces Conf^n(X)={(x_1,...,x_n): x_i\neq x_j for i\neq j} / S_n. We present a rational function in two variables from whose coefficients we can read off the i-th Betti numbers of Conf^n(X) for all i and n. The key of the proof is a property called "purity", which was known to Kim for (ordered or unordered) configuration spaces of the complex plane with r >= 0 points removed. We show that the unordered configuration spaces of X also have purity (but with different weights). This is a joint work with G. Cheong.   See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Sep 18

IMA/MCIM Industrial Problems Seminar

1:25pm - Online
SIAM Internship Panel
Montie Avery, University of Minnesota, Twin Cities
Abstract:

The event will have graduate students speaking about their experiences with their internships.

The facilitator of the event is Montie Averie.

The participants of the Graduate Student Internship Panel will be:

Carter Chain (interned at Travelers)

Brendan Cook (interned at Target)

Ty Frazier (interned at Securian Financial and Lawrence Berkeley national lab)

Sarah Milstein (interned at Ayasdi, 3M, IDA, Cargill and Smart Information Flow Technologies (SIFT))

Amber Yuan (interned at Argonne national lab,  ExxonMobil  and Activision Blizzard).

The event is organized by the SIAM Student Chapter at the University of Minnesota.

Thu Sep 17

Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
25 years since Fermat's Last Theorem
Frank Calegari, University of Chicago
Abstract:

Wiles's proof of Fermat's Last Theorem was published 25 years ago. Wiles's paper introduced many new ideas and methods which have since shaped the field of algebraic number theory. This colloquium talk intends to give a (biased) tour of these developments, especially with regard to questions that might be of interest to non-specialists.

Thu Sep 17

11:15am - Zoom
Climate Seminar
TBA
Wed Sep 16

Probability Seminar

4:00pm - Via Zoom
Tail bounds for the averaged empirical distribution on a geodesic in first-passage percolation
Wai-Kit Lam, UMN
Abstract:

Consider $\mathbb{Z}^d$ with nearest-neighbor edges. In first-passage percolation, we place i.i.d. nonnegative weights $(t_e)$ on the edges, and study the induced graph metric $T(x,y)$. A geodesic is a minimizing path for this metric. In a joint work with M. Damron, C. Janjigian and X. Shen, we study the empirical distribution on a geodesic $\gamma$ from $0$ to $x$: $\nu^x(B) := (number of edges e in \gamma with t_e \in B) / (number of edges e in \gamma)$. We establish bounds for the averaged empirical distribution $E \nu^x(B)$, particularly showing that if the law of $t_e$ has finite moments of any order strictly larger than 1, then roughly speaking the limiting averaged empirical distribution has all moments.

Wed Sep 16

AMS Intro to Research Seminar

12:20pm - Zoom
Vegetation patterns in dryland ecosystems
Paul Carter
Abstract:

In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. The dynamics of these patterns can be modeled by reaction-diffusion PDEs describing the interplay of vegetation and water resources, where sloped terrain is modeled through advection terms representing the downhill flow of water. We focus on one such model in the 'large-advection' limit, and we prove the existence of traveling planar stripe patterns using analytical and geometric techniques. We also discuss implications for the stability of the resulting patterns, as well as the appearance of curved stripe solutions.

Tue Sep 15

Dynamical Systems

2:30pm - Zoom - see link below
Dynamical systems for metabolic networks
Nicola Vassena, Free University Berlin
Abstract:

In this talk I will give an overview of one approach to the analysis of metabolic networks, using dynamical systems. When considered in applications, one of the main features of these networks is that the interaction functions (reaction rates) are practically unknown. That is, the most reliable data is the structure of network. For this reason, we present here a qualitative approach based on the structure of the network, only, where no quantitative information is needed. In particular, following this approach, we introduce how to address some bifurcation problems and sensitivity analysis.

https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Sep 15

11:15am - Zoom
Climate Seminar
TBA
Mon Sep 14

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 14

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Sep 14

Special Events and Seminars

11:00am - https://umn.zoom.us/j/91467804294
"Harmonic Analysis-Geometric Measure Theory-Partial Differential Equations Seminar"
Bruno Poggi Cevallos, University of Minnesota
Fri Sep 11

Combinatorics Seminar

3:35pm - Zoom ID is 941-2794-9847
Order Polynomial Product Formulas and Poset Dynamics
Sam Hopkins
Abstract:

I'll present a heuristic for finding special families of partially ordered sets. The heuristic says that the posets with order polynomial product formulas are the same as the posets with good dynamical behavior. Here the order polynomial is a certain enumerative invariant of the poset. Meanwhile, the dynamics includes promotion of linear extensions, and rowmotion of order ideals and P-partitions. This talk includes joint work with Tri Lai, and with Martin Rubey.

see seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Fri Sep 11

IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Flying High with Math
Sharon Arroyo, Shabnam Khamooshi, The Boeing Company, The Boeing Company
Abstract:

Sharon and Shabnam are members of Boeing Research & Technology. They partner with business units to develop operations research based solutions and mathematical tools that help Boeing reduce costs, improve products and operations. They have developed operations research and math solutions as well as simulation models for applications across Boeing including supply chain, aircraft delivery, airline scheduling, wind tunnel testing, robot scheduling, logistics, communication networks, sensor fusion, rate analysis, and facility layout design. In this presentation, Sharon and Shabnam will give an overview of some of the projects on which they have worked and will give insights into what it is like to work as a mathematician in industry.

Sharon Arroyo
Sharon is a Technical Fellow in the Applied Mathematics Group at Boeing and the technical lead for operations research. She partners with business units to develop operations research based solutions and mathematical tools that help Boeing reduce costs, improve products and operations. She has developed operations research and math solutions for applications across Boeing including supply chain, airline scheduling, wind tunnel testing, aircraft delivery, robot scheduling, logistics, communication networks, and sensor fusion and scheduling. Prior to joining Boeing, she was an Assistant Professor at Iowa State University. She received her B.S. in Mathematics from Stanford University and her M.S. and Ph.D. in Operations Research from Cornell University.

Shabnam Khamooshi
Shabnam joined the Boeing Company in 2013 after finishing her post doctorate fellowship at the University of Washington. Her work was mainly focused on optimization and operations research projects including transportation and logistics optimization as well as layout planning optimization and simulation. She received her PhD from University of Houston and her dissertation was on optimizing the transportation system for hurricane evacuation (research funded by the Department of Homeland Security). Currently, she works in the BR&T Production Analytics team on a variety of projects including airplane delivery schedule optimization, airplane stall allocation optimization and production scheduling. Her main area of interest is applying operations research, mathematical modeling, and statistical analysis in all areas of airplane life cycle.

Thu Sep 10

Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
Kinetic theory of structured populations: demographics, cell size control, and stochastic hierarchies
Tom Chou, University of California, Los Angeles
Abstract:

We will briefly review, through two examples, classic deterministic PDE models of population dynamics structured according to attributes such as age and/or size. First, we describe how the original McKendrick model was used to motivate China's one-child policy, and generalize it to include an imposed, finite interbirth refractory period. We quantify the effectiveness of this softer, staggered birth policy and discuss its predicted effectiveness. We then review sizer-timer-adder-type models used to quantify proliferating cell populations. Here, blow-up in mean cell sizes can arise, which represents a challenging numerical problem. Finally, we extend these classic deterministic models to allow for both demographic and growth-rate stochasticity by developing a fully kinetic theory. Marginalization of the full density functions results in a set of coupled kinetic models similar to the BBGKY hierarchy. We map out the different combinations of stochastic descriptions and show how the classic age-dependent population models are connected to this hierarchy, the lowest order of which is a master equation for the total stochastic population. Differences in the stochastic description of birth through budding or splitting are explored.

Wed Sep 09

Probability Seminar

4:00pm - Via Zoom
NU-UMN Joint Probability Seminar

Wed Sep 09

Special Events and Seminars

11:00am - https://umn.zoom.us/j/99821709760
Hessian Estimates for the Lagrangian mean curvature equation
Arunima Bhattacharya, University of Washington, Washington
Abstract:

In this talk, we will derive a priori interior Hessian estimates for the Lagrangian mean curvature equation under certain natural restrictions on the Lagrangian phase. As an application, we will use these estimates to solve the Dirichlet problem for the Lagrangian mean curvature equation with continuous boundary data, on a uniformly convex, bounded domain in R^n.

Tue Sep 08

Dynamical Systems

2:30pm - Via Zoom
Dynamical Systems Seminar

Mon Sep 07

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 07

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Aug 31

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 31

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Aug 24

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 24

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Tue Aug 18

IMA Data Science Lab Seminar

1:25pm - Zoom
Fairness, Accountability, and Transparency: (Counter)-Examples from Predictive Models in Criminal Justice
Kristian Lum, University of Pennsylvania
Abstract:

The need for fairness, accountability, and transparency in computer models that make or inform decisions about people has become increasingly clear over the last several years. One application area where these topics are particularly important is criminal justice, as statistical models are being used to make or inform decisions that impact highly consequential decisions those concerning an individuals freedom. In this talk, Ill highlight three threads of my own research into the use of machine learning and a statistical models in criminal justice models that demonstrate the importance of careful attention to fairness, accountability, and transparency. In particular, Ill discuss how predictive policing has the potential to reinforce and amplify unfair policing practices of the past. Ill also discuss some of the ways in which recidivism prediction models can fail to require the accountability and transparency necessary to prevent gaming.

Kristian Lum is on the faculty at University of Pennsylvania's School of Engineering and Applied Science and is the former Lead Statistician at the Human Rights Data Analysis Group (HRDAG). Kristians research primarily focuses on examining the uses of machine learning in the criminal justice system, including demonstrating the potential for predictive policing models to reinforce and amplify historical racial biases in law enforcement. She has also served on Research Advisory Councils for the New York Citys Mayors Office of Criminal Justice and Philadelphias First Judicial District tasked with advising on the development of fairer algorithmic pre-trial risk assessments.

Kristian holds an M.S. and Ph.D. from the Department of Statistical Science at Duke University and a B.A. in Mathematics and Statistics from Rice University.

Mon Aug 17

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 17

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Aug 10

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 10

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Tue Aug 04

IMA Data Science Lab Seminar

1:25pm - Zoom
Lecture
Anil Vullikanti, University of Virginia
Tue Aug 04

IMA Data Science Lab Seminar

1:25pm - Lind Hall 305
A Network Science Approach for Controlling Epidemic Outbreaks
Anil Vullikanti, University of Virginia
Abstract:

The spread of epidemics is a very complex process, and stochastic diffusion models on networks have been found useful, especially when modeling their spread in large and heterogeneous populations, where individual and community level behaviors need to be represented. A fundamental problem in such models is to understand how to control the spread of an epidemic by interventions such as vaccination (which can be modeled as node removal) and social distancing (which can be modeled as edge removal). A number of heuristics have been studied, such as selecting nodes based on degree and eigenscore. However, rigorous algorithms with approximation guarantees are not well understood, and is the focus of this talk.

We will discuss two approaches for epidemic control from a network science perspective. The first involves reducing the spectral radius of the graph, motivated by a characterization that shows that epidemics in some models die out fast if the spectral radius is below a threshold. We discuss algorithms for this problem and its generalizations. The second approach involves stochastic optimization, using a sample average approximation combined with rounding. We show that this approach gives near optimal solutions in practice, and have interesting structural properties, which might be useful
in finding practical interventions.

Anil Vullikanti is a Professor in the Department. of Computer Science and the Biocomplexity Institute at the University of Virginia. His research interests are in the broad areas of network science, dynamical systems, combinatorial optimization, and distributed computing, and their applications to computational epidemiology and social networks.

Mon Aug 03

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 03

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Jul 27

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 27

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Jul 20

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 20

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Jul 13

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 13

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Jul 06

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 06

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Jun 29

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 29

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Tue Jun 23

IMA Data Science Lab Seminar

1:25pm - Online
Computational Science for COVID-19 Pandemic Planning and Response
Abstract:

The ongoing COVID-19 pandemic represents an unprecedented global crisis.
Increased urbanization, global travel, climate change and a generally older and immuno-compromised population continue to make the problem of pandemic planning and control challenging. Recent advances in computing, AI and data science have created new opportunities for realizing the vision of real-time epidemic science.

In this talk, using COVID-19 as an exemplar,
I will describe how computing and data science can play an important
role in developing and assessing pandemic response strategies.

Madhav Marathe is the division director of the Networks Simulation
Science and Advanced Computing Division at the Biocomplexity Institute
and Initiative, and a professor in the Department of Computer Science
at the University of Virginia. His research interests are in network
science, foundations of computing, Human and engineered intelligence
at scale, computational epidemiology, socially coupled system science
and high performance computing. Before joining UVA, he held positions
at Virginia Tech and Los Alamos National Laboratory. He is a Fellow
of the IEEE, ACM, SIAM and AAAS.

Mon Jun 22

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 22

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Jun 15

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 15

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Tue Jun 09

IMA Data Science Lab Seminar

1:25pm - Online
Data and Models for COVID-19 Decision-Making
Forrest Crawford, Yale University
Abstract:

As states begin to reopen, there is an urgent need for
COVID-19 projections that can guide decision-makers in relaxing
restrictions in a way that minimizes the chance of resurgence. Though
disease transmission models, limited data and uncertainties about
epidemiological features of COVID-19 make statistical calibration of
these models challenging. Futhermore, decision-makers are often more
interested in future projections under specified re-opening scenarios
than in estimated parameter values. In this presentation, I outline
mathematical and statistical approaches for projecting COVID-19
incidence, hospitalization, and deaths. I describe a simple class of
transmission models that balance parsimony with epidemiological
from Connecticut, and information about the Governor's stated
reopening plans, we find that closure of schools and the statewide
Stay Safe, Stay Home order have effectively reduced COVID-19
transmission in Connecticut, with model projections estimating
incidence at about 1,500 new infections per day. If close
interpersonal contact increases quickly in Connecticut following
reopening on May 20, the state is at risk of a substantial increase
COVID-19 infections, hospitalizations, and deaths by late Summer 2020.
However, real-time metrics including case counts, hospitalizations,
and deaths may fail to provide enough advance warning to avoid
resurgence. Substantial uncertainty remains in our knowledge of
cumulative COVID-19 incidence, the proportion of infected individuals
who are asymptomatic, infectiousness of children, the effects of
testing and contact tracing on isolation of infected individuals, and
how contact patterns may change following reopening.

Mon Jun 08

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 08

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Jun 01

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 01

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Thu May 28

Analysis and PDE Working Seminar

Analysis and PDE Working Seminar
Gianmarco Brocchi, University of Birmingham
Tue May 26

Analysis and PDE Working Seminar

Analysis and PDE Working Seminar
&nbsp;<b>&nbsp;</b>Lisa Naples&nbsp;, University of Connecticut

Mon May 25

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon May 25

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri May 22

IMA/MCIM Industrial Problems Seminar

1:25pm - Online
AI for COVID-19: An Online Virtual Care Approach
Xavier Amatriain, Curai
Abstract:

With half of the worlds population lacking access to healthcare services, and 30% of the adult population in the US having inadequate health insurance coverage to get even basic access to services, it should have been clear that a pandemic like COVID-19 would strain the global healthcare system way over its maximum capacity. In this context, many are trying to embrace and encourage the use of telehealth as a way to provide safe and convenient access to care. However, telehealth in itself can not scale to cover all our needs unless we improve scalability and efficiency through AI and automation.

In this talk, we will describe how our work on combining latest AI advances with medical experts and online access has the potential to change the landscape in healthcare access and provide 24/7 quality healthcare. Combining areas such as NLP, vision, and automatic diagnosis we can augment and scale doctors. We will describe our work on combining expert systems with deep learning to build state-of-the-art medical diagnostic models that are also able to model the unknowns. We will also show our work on using language models for medical Q&A . More importantly, we will describe how those approaches have been used to address the urgent and immediate needs of the current pandemic.

Xavier Amatriain is co-founder/CTO of Curai, a startup using AI to scale the worlds best healthcare to every human being. Prior to this, he was VP of Engineering at Quora, and Research/Engineering Director at Netflix, where he led the team building the famous Netflix recommendation algorithms. Before going into leadership positions in industry, Xavier was a researcher in both academia and industry. With over 50 publications in different fields, Xavier is best known for his work on machine learning in general and recommender systems in particular. He has lectured at different universities both in the US and Spain and is frequently invited as a speaker and senior committee member at conferences.

Thu May 21

Analysis and PDE Working Seminar

Analysis and PDE Working Seminar
Wenjie Lu, University of Minnesota
Tue May 19

IMA Data Science Lab Seminar

1:25pm - Online
Transmission Dynamics of Influenza and SARS-CoV-2: Environmental Determinants, Inference and Forecast
Jeffrey Shaman, Columbia University
Abstract:

Dynamic models of infectious disease systems are often used to study the epidemiological characteristics of disease outbreaks, the ecological mechanisms and environmental conditions affecting transmission, and the suitability of various mitigation and intervention strategies. In recent years these same models have been employed to generate probabilistic forecasts of infectious disease incidence at the population scale. Here I present research from my own group describing investigation of the environmental determinants of influenza transmissibility and development of model systems and combined model-inference frameworks capable of simulation, inference and forecast of disease outbreaks with a particular focus on influenza and SARS-CoV-2.

Mon May 18

Analysis and PDE Working Seminar

Analysis and PDE Working Seminar
Jack Burkart, Stony Brook University
Mon May 18

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon May 18

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Tue May 12

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon May 11

Analysis and PDE Working Seminar

Analysis and PDE Working Seminar
Guillermo Rey, Wing
Mon May 11

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon May 11

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri May 08

Combinatorics Seminar

3:35pm - the talk will talk place at this Zoom link, at
Troupes and Cumulants
Colin Defant, Princeton
Abstract:

Cumulants are the fundamental combinatorial tools used in noncommutative probability theory. Sequences of free cumulants and sequences of classical cumulants are paired with each other via summation formulas involving partition lattices and noncrossing partition lattices. In several cases, a sequence of free cumulants that counts a set of colored binary plane trees happens to correspond, somewhat miraculously, to a sequence of classical cumulants that counts the decreasing labeled versions of the same trees. We will see that this strange phenomenon holds for families of trees that we call troupes, which are defined using two new operations on colored binary plane trees that we call insertion and decomposition. Troupes also provide a broad framework for generalizing several of the results that are known about West's stack-sorting map. We will hint at just a couple of the many ways in which the investigation of troupes could be extended further. the talk will talk place at this Zoom link, at 3:35 CDT.

Fri May 08

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri May 08

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri May 08

1:30pm - Vincent Hall 364

Fri May 08

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri May 08

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar

Thu May 07

3:35pm - VinH 16
Colloquium
Cancelled
Thu May 07

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu May 07

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed May 06

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Wed May 06

PDE Seminar

3:35pm - Vincent Hall 570 ,
PDE Seminar - Cancelled

Tue May 05

3:30pm - VinH 16
Colloquium

Tue May 05

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue May 05

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue May 05

IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Svetlana Lazebnik, University of Illinois at Urbana-Champaign
Tue May 05

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon May 04

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium
Eric Bonnetier, Université Joseph Fourier
Mon May 04

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon May 04

Analysis and PDE Working Seminar

3:35pm - TBA
Analysis & PDE Working Seminar
Ryan Matzke
Mon May 04

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon May 04

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon May 04

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri May 01

Combinatorics Seminar

3:35pm - Zoom id 391-940-053
Associahedra, Cyclohedra, and inversion of power series
Jose Bastidas
Abstract:

Abstract: Species and Hopf monoids are powerful algebraic tools to study families of combinatorial structures. Aguiar and Ardila introduced the Hopf monoid of generalized permutahedra and realized many combinatorial Hopf monoids as submonoids of generalized permutahedra. They solved the antipode problem for the Hopf monoid of associahedra and explained how the classical Lagrange inversion formula for power series follows from this. In this talk, we bring cyclohedra into the picture. We solve the antipode problem for this new Hopf monoid and use this result to describe inversion in a group of pairs of power series using the face structure of associahedra and cyclohedra. The talk is based on joint work with Marcelo Aguiar (Cornell University).

Fri May 01

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri May 01

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri May 01

1:30pm - Vincent Hall 364

Fri May 01

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri May 01

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Thu Apr 30

3:35pm - VinH 16
Colloquium
Cancelled
Thu Apr 30

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Apr 30

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed Apr 29

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Wed Apr 29

PDE Seminar

3:30pm - Vincent Hall 570 ,
PDE Seminar - Cancelled

Tue Apr 28

3:30pm - VinH 16
Colloquium

Tue Apr 28

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Apr 28

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Apr 28

IMA Data Science Lab Seminar

1:25pm - Lind 305
Detecting New Signals Under Background Mismodeling
Sara Algeri, University of Minnesota, Twin Cities
Abstract:

When searching for new astrophysical phenomena, uncertainty arising from background mismodeling can dramatically compromise the sensitivity of the experiment under study. Specifically, overestimating the background distribution in the signal region increases the chances of missing new physics. Conversely, underestimating the background outside the signal region leads to an artificially enhanced sensitivity and a higher likelihood of claiming false discoveries. The aim of this work is to provide a unified statistical algorithm to perform modeling, estimation, inference and signal characterization under background-mismodeling. The method proposed allows to incorporate the (partial) scientific knowledge available on the background distribution, and provides a data-updated version of it in a purely nonparametric fashion, without requiring the specification of prior distributions. If a calibration sample or control regions are available, the solution discussed does not require the specification of a model for the signal; however, if the signal distribution is known, it allows to further improve the accuracy of the analysis and to detect additional signals of unexpected new sources.

Tue Apr 28

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Apr 27

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Apr 27

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Apr 27

Analysis and PDE Working Seminar

PDE aspects of the Navier-Stokes equations
Dallas Albritton
Abstract:

This will be an expository talk on PDE aspects of the Navier-Stokes equations.Zoom link. https://umn.zoom.us/j/92809219308

Mon Apr 27

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 27

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Apr 27

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Apr 24

MCFAM Distinguished Lecture Series

5:30pm - VinH 16
MCFAM Distinguished Lecture Series - Cancelled

Fri Apr 24

Combinatorics Seminar

3:35pm - Zoom ID 391-940-053
Coxeter factorizations and the Matrix Tree theorem with generalized Jucys-Murphy weights
Theo Douvropolous
Abstract:

One of the most far reaching proofs of Cayley's formula, that the number n^{n-2} counts trees on n labeled vertices, is via Kirchhoff's Matrix Tree theorem. After Denes, Schaeffer, and many others, there is a well-exploited correspondence between trees and transitive factorizations in the symmetric group; in particular, the number n^{n-2} counts shortest factorizations of the long cycle (12..n) in transpositions. Furthermore, Burman and Zvonkine (and independently Alon and Kozma) have given a "higher-genus" formula that enumerates arbitrary length factorizations of long cycles, where each transposition (ij) is weighted by its own variable w_ij, and which has a product form involving the eigenvalues of the Laplacian L(K_n) of the complete graph.In joint work with Guillaume Chapuy, we consider a (partial) analog of the weighted Laplacian for complex reflection groups W. The weights are specified via any given flag of parabolic subgroups, generalizing the definition of Jucys-Murphy elements. We prove a product formula for the enumeration of weighted reflection factorizations of Coxeter elements, that subsumes the Chapuy-Stump formula and in part the Burman-Zvonkine formula. Its proof is based on an interesting fact that relates the exterior powers of the reflection representation with those W-characters that are non-zero on the Coxeter class. We present some further applications of these techniques, in particular, a uniform simple(r) way to produce the chain number h^n*n!/|W| of the noncrossing lattice NC(W). An extended abstract for this work was accepted for FPSAC 2020 and is available at my website (https://www.irif.fr/~douvr001/).

Fri Apr 24

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Apr 24

Probability Seminar

2:30pm - Vincent Hall 213
Rotationally invariant \alpha-stable stochastic processes with some membranes located on a given surface
M. Portenko, Institute of mathematics, Nat. Acad. Sci. Ukraine, Kyiv.
Abstract:

Two kinds of singular transformations of a rotationally invariant \alpha-stable process (x(t))_{t \ge 0} in a d-dimensional Euclidean space R^d are considered. They are both connected with the notion of a local time on a given surface S in R d for the process (x(t))_{t \ge 0} (it is supposed that \alpha \in (1, 2) and d \ge 2). The first transformation is determined by a given continuous function (p(x))_{x \in S} with non-negative values and it consists in killing the process (x(t))_{t \ge 0} at a point x \in S with the intensity p(x). This kind of membranes can be called an elastic screen by analogy to that in the theory of diffusion processes. The second transformation is likewise determined by a given function (p(x))_{x \in S} with positive values and its result is the process (x(t))_{t \ge 0} for which any point x \in S is sticky with the intensity r(x). It is shown that each one of these membranes is associated with some initial-boundary value problem for a pseudo-differential equation related to the process (x(t))_{t \ge 0}. These facts are established with the help of some generalization of classical theory of single-layer potentials for situations where, instead of differential, the pseudo-differential equation mentioned above is considered.

Fri Apr 24 2:30pm - Walter B28
Unicode test ?

Fri Apr 24

1:30pm - Vincent Hall 364

Fri Apr 24

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Apr 24 1:00pm - Walter B28
Django22 Test

Fri Apr 24

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Thu Apr 23

3:35pm - VinH 16
Colloquium
Cancelled
Thu Apr 23

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Apr 23

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed Apr 22

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Wed Apr 22

PDE Seminar

3:30pm - Vincent Hall 570 ,
PDE Seminar - Cancelled

Tue Apr 21

3:30pm - VinH 16
Colloquium

Tue Apr 21

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Apr 21

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Apr 21

IMA Data Science Lab Seminar

1:25pm - Lind 305
LECTURE CANCELED
-, -
Tue Apr 21

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Apr 20

Applied and Computational Math Colloquium

3:35pm - Zoom Meeting: https://umn.zoom.us/j/531493431
Numerical Methods for the Optimal Transport Problem
Brittany Hamfeldt, New Jersey Institute of Technology
Abstract:

The problem of optimal transportation, which involves finding the most cost-efficient mapping between two measures, arises in many different applications. However, the numerical solution of this problem remains extremely challenging and standard techniques can fail to compute the correct solution. Recently, several methods have been proposed that obtain the solution by solving the Monge-Ampere equation, a fully nonlinear elliptic partial differential equation (PDE), coupled to a non-standard implicit boundary condition. Unfortunately, standard techniques for analyzing numerical methods for fully nonlinear elliptic equations fail in this setting. We introduce a modified PDE that couples the usual Monge-Ampere equation to a Hamilton-Jacobi equation that restricts the transportation of mass. This leads to a simple framework for guaranteeing that a numerical method will converge to the true solution, which applies to a large class of approximation schemes. We describe some simple examples. A range of challenging computational examples demonstrate the effectiveness of this method, including the recent application of these methods to problems in beam shaping and seismic inversion.https://umn.zoom.us/j/531493431

Mon Apr 20

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Apr 20

Analysis and PDE Working Seminar

3:35pm - Vincent Hall 6
Analysis & PDE Working Seminar
Dallas Albritton
Mon Apr 20

Analysis and PDE Working Seminar

Introduction to the Lp theory of stochastic PDEs
&nbsp;Timur Yastrzhembskiy&nbsp;&nbsp;
Abstract:

I will overview the Lp-theory of parabolic stochastic partial differential equations (SPDEs) on the whole space developed by N.V. Krylov in the 90s. If time permits, I will discuss the well-posedness of SPDEs driven by space-time white noise. Such equations are quite popular in the literature. The talk is aimed at people familiar with the theory of PDEs. Little knowledge of probability is assumed.Zoom link.  https://umn.zoom.us/j/99241065966

Mon Apr 20

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 20

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Apr 20

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Apr 17

MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar
MFM Modeling Workshop Presenations, University of Minnesota
Fri Apr 17

Combinatorics Seminar

3:35pm - Zoom ID 391-940-053
A combinatorial e-expansion of vertical-strip LLT polynomials
Abstract:

In 2019, D'Adderio proved that if G(x;q) is a vertical-strip LLT polynomial, then G(x;q+1) is positive in the elementary symmetric functions basis. A conjectured formula
for the coefficients in this basis was given earlier in 2019 by Alexandersson. We give a new proof of D'Adderio's result which also proves the conjectured formula.

The problem of finding such an e-expansion is surprisingly similar to the still open problem of Shareshian-Wachs, regarding the e-expansion of chromatic polynomials associated with unit-interval graphs. We shall discuss this connection as well.

Fri Apr 17

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Apr 17

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Apr 17

1:30pm - Vincent Hall 364

Fri Apr 17

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Apr 17

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Thu Apr 16

3:35pm - VinH 16
Colloquium

Thu Apr 16

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Apr 16

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed Apr 15

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Local Densities of Diagonal Integral Ternary Quadratic Forms at Odd Primes
Edna Jones, Rutgers University
Abstract:

We give formulas for local densities of diagonal integral ternary quadratic forms at odd primes. Exponential sums and quadratic Gauss sums are used to obtain these formulas. These formulas (along
with 2-adic densities and Siegel's mass formula) can be used to compute the representation numbers of certain ternary quadratic forms.

Wed Apr 15

PDE Seminar

3:30pm - Vincent Hall 570 ,
PDE Seminar - Cancelled

Wed Apr 15

IMA Data Science Lab Seminar

10:10am - Lind 305
LECTURE CANCELED
Andrea Montanari, Stanford University
Tue Apr 14

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Apr 14

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Apr 14

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Apr 14

IMA Data Science Lab Seminar

1:25pm - Lind 305
LECTURE CANCELED
-, -
Tue Apr 14

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Apr 13

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium - Cancelled
Dio Margetis, Maryland
Mon Apr 13

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Apr 13

Analysis and PDE Working Seminar

The boundary value problems in higher codimension
Zanbing Dai
Abstract:

The boundary value problems have been studied for decades. People first studied boundary value problems for the Laplace operator on bounded Lipschitz domains. Using a change of variable argument, we can map Lipschitz domains onto the upper half plane $\mathbb{R}^{d+1}_+$ and converts Laplace operator into a second order elliptic divergence operator, whose coefficient satisfies a certain smoothness condition, the Carleson measure condition. Recently, David, Feneuil and Mayboroda developed an elliptic theory in higher co- dimension. They studied a particular degenerate second order elliptic operator $L={\rm div} A\nabla$. Now, the domain we are interested in has more than one non-tangential direction. In this talk, I will focus on flat domain $\mathbb{R}^n\setminus \mathbb{R}^d$ and introduce the Dirichlet results, which has been proved recently. Finally, I will introduce my project on the regularity problem in higher codimension.

Mon Apr 13

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 13

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Apr 13

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Apr 10

MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar Cancelled

Fri Apr 10

Combinatorics Seminar

3:35pm - The talk will take place at https://umn.zoom.us/
Combinatorics Seminar
Abstract:

The {\em Vandermonde determinant} is ubiquitous in algebraic combinatorics and representation theory. One application of the Vandermonde is as a generator for a harmonic' model of the coinvariant ring attached to the symmetric group which eschews the use of -- and computational issues involved with -- quotient rings. We present an extension of the Vandermonde determinant to {\em superspace} (a symmetric algebra tensor an exterior algebra) and use it to generate a variety of modules including the recently defined Delta Conjecture coinvariant rings' of Haglund-Rhoades-Shimozono as well as (conjecturally) a trigraded module for the full Delta Conjecture. We use superspace Vandermondes to build bigraded superspace quotients tied to the geometry of {\em spanning configurations} studied by Pawlowski-Rhoades which satisfy a superspace version of Poincar\'e Duality and (conjecturally) exhibit unimodality properties which suggest a superspace version of Hard Lefschetz. Joint with Andy Wilson.

Fri Apr 10

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Apr 10

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Apr 10

1:30pm - Vincent Hall 364

Fri Apr 10

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Apr 10

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Thu Apr 09

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Apr 09

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Apr 09

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed Apr 08

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Wed Apr 08

PDE Seminar

3:35pm - Vincent Hall 570 ,
PDE Seminar - Cancelled

Tue Apr 07

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Apr 07

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Apr 07

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Apr 07

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Apr 06

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Apr 06

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Apr 06

Analysis and PDE Working Seminar

3:35pm - VinH 301
Analysis & PDE Working Seminar
Timur Yastrzhembskiy
Mon Apr 06

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 06

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Apr 06

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Apr 03

MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar Cancelled

Fri Apr 03

Combinatorics Seminar

3:35pm - Zoom id 391-941-053, available by clicking her
The box-ball system and cyclindric loop Schur functions
Gabe Frieden, UQAM
Abstract:

The box-ball system is a cellular automaton in which a sequence of balls moves along a row of boxes. An interesting feature of this automaton is its soliton behavior: regardless of the initial state, the balls in the system eventually form themselves into connected blocks (solitons) which remain together for the rest of time.

In 2014, T. Lam, P. Pylyavskyy, and R. Sakamoto conjectured a formula which describes the solitons resulting from an initial state of the box-ball system in terms of the tropicalization of certain polynomials they called cylindric loop Schur functions. In this talk, I will describe the various ingredients of this conjecture and discuss its proof.

Fri Apr 03

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Apr 03

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Apr 03

1:30pm - Vincent Hall 364

Fri Apr 03

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Apr 03

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Thu Apr 02

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Apr 02

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Apr 02

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed Apr 01

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Wed Apr 01

PDE Seminar

3:35pm - Vincent Hall 570 ,
PDE Seminar - Cancelled

Tue Mar 31

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 31

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Mar 31

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Mar 31

IMA Data Science Lab Seminar

1:25pm - Lind 305
LECTURE CANCELED
-, -
Tue Mar 31

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Mar 30

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Mar 30

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Mar 30

Analysis and PDE Working Seminar

Mathematical foundations of slender body theory
Laurel Ohm
Abstract:

Slender body theory (SBT) facilitates computational simulations of thin filaments in a 3D viscous fluid by approximating the hydrodynamic effect of each fiber as the flow due to a line force density along a 1D curve. Despite the popularity of SBT in computational models, there had been no rigorous analysis of the error in using SBT to approximate the interaction of a thin fiber with fluid. In this talk, we develop a PDE framework for analyzing the error introduced by this approximation. In particular, given a 1D force along the fiber centerline, we define a notion of true solution to the full 3D slender body problem and obtain an error estimate for SBT in terms of the fiber radius. This places slender body theory on firm theoretical footing. We also present similar estimates in case of free-ended and rigid filaments.

Mon Mar 30

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Mar 30

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Mar 30

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Mar 27

MCFAM Seminar

5:30pm - Vincent Hall 16
Social Determinants of Health
Shae Armstrong, Optum
Fri Mar 27

MCFAM Seminar

5:30pm - Vincent Hall 16
No MCFAM Seminar

Fri Mar 27

Combinatorics Seminar

3:35pm - Via Virtual - Zoom
Counting trees and nilpotent endomorphisms
Vic Reiner
Abstract:

A formula of Cayley (1889) says that the number of trees on vertex set [n]:={1,2,...,n} is n^{n-2}. Among its many proofs, my favorite is a gorgeous bijection due to Andre Joyal in 1981. One can also view Cayley's formula as asserting that there are n^{n-1} vertex-rooted trees on [n], or equivalently n^{n-1} eventually constant self-maps on [n].

This talk will review Joyal's proof, and its recent revisitation by Tom Leinster in arXiv:1912.12562. Leinster gives a beautiful q-analogue of the proof, that proves a q-analogous theorem of Fine and Herstein (1958). The latter theorem counts those linear self-maps of an n-dimensional vector space over a finite field F_q which are eventually constant, that is, nilpotent as linear maps.

Fri Mar 27

Analysis and PDE Working Seminar

3:35pm - Vincent Hall 6
Analysis and PDE Working Seminar

Fri Mar 27

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Mar 27

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Mar 27

1:30pm - Vincent Hall 364

Fri Mar 27

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
CANCELED--The Technical and Organizational Challenges of Data Science
Catherine (Katy) Micek, 3M
Abstract:

In October 2012  shortly after I began my career in the data science space  the Harvard
Business Review published the article Data Scientist: The Sexiest Job of the 21st Century and
generated an enormous amount of buzz about the field. Since then, data science has matured:
technical skill sets required to do the work are better defined and specializations are emerging.
However, the field is still evolving and how data science is used by an organization can vary
greatly. In such a dynamic and broadly defined field, it has been my experience that data
scientists need to have a wide range of technical skills augmented by soft skills in order to be
successful. In this talk, I will share my experience working as a predictive modeler, data
scientist, and software developer across various industries (insurance, energy, and within 3M),
as well as provide examples of challenges Ive encountered as a data scientist. I will also discuss
my work on a Digital Solutions Implementation for 3Ms Knoxville plant, a project where we are
exploring how data science to understand and reduce product variability for Acrylic Foam Tape.

Catherine (Katy) Micek is a Data Scientist at 3M in St. Paul, Minnesota. She holds a Ph.D.
in Applied Mathematics from the University of Minnesota. In her Ph.D. thesis, Katy developed
mathematical models for polymer gel swelling with applications to artificial bone implants and
drug-delivery devices. Katy has worked in both academic and industrial positions since
earning her degree. In addition to teaching college mathematics, she has worked on crossfunctional business teams as a data scientist, software developer, and predictive modeler
teams across diverse industries (insurance, energy, finance, supply chain, and manufacturing).
Katy is also an active speaker and mentor. She is frequently invited to college, universities,
and conferences to discuss her technical work and career experiences in data science, and
she is a contributor to publications by the Society of Industrial and Applied Mathematics on
industrial career options. In her free time, Katy enjoys spending time with friends and family,
as well as ballroom dancing, rock climbing, and cooking.

Fri Mar 27

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Mar 27

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Thu Mar 26

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Mar 26

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Mar 26

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed Mar 25

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Wed Mar 25

PDE Seminar

3:35pm - Vincent Hall 570 ,
PDE Seminar - Cancelled

Tue Mar 24

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 24

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Mar 24

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Mar 24

IMA Data Science Lab Seminar

1:25pm - Lind 305
CANCELED--Kernel Approaches in Global Statistical Distances, Local Measure Detection, and Active Learning
-, -
Abstract:

In this talk, we'll discuss the problem of constructing meaningful distances between probability distributions given only finite samples from each distribution. We approach this through the use of data-adaptive and localized kernels, and in a variety of contexts. First, we construct locally adaptive kernels to define fast pairwise distances between distributions, with applications to unsupervised clustering. Then, we construct localized kernels to determine a statistical framework for determining where two distributions differ, with applications to measure detection for generative models. Finally, we'll begin to address the question of measure detection without a priori known labels of which distribution a point came from. This is addressed through active learning, in which one can choose a small number of points at which to query a label. This is ongoing work with Xiuyuan Cheng (Duke) and Hrushikesh Mhaskar (CGU), among others.

Alex Cloninger is an Assistant Professor in the Mathematics Department and the Hal?c?o?lu Data Science Institute at UCSD. He received his PhD in Applied Mathematics and Scientific Computation from the University of Maryland in 2014, and was then an NSF Postdoc and Gibbs Assistant Professor of Mathematics at Yale University until 2017, when he joined UCSD. Alex researches problems around the analysis of high dimensional data. He focuses on approaches that model the data as being locally lower dimensional, including data concentrated near manifolds or subspaces. These types of problems arise in a number of scientific disciplines, including imaging, medicine, and artificial intelligence, and the techniques developed relate to a number of machine learning and statistical algorithms, including deep learning, network analysis, and measuring distances between probability distributions.

Tue Mar 24

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Mar 23

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Mar 23

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Mar 23

Analysis and PDE Working Seminar

3:35pm - Vincent Hall 6
Analysis & PDE Working Seminar

Mon Mar 23

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Mar 23

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Mar 23

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Mar 20

MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar - No Seminar

Fri Mar 20

Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar - Cancelled
Gabriel Frieden
Fri Mar 20

Analysis and PDE Working Seminar

3:35pm - Vincent Hall 6
Analysis and PDE Working Seminar

Fri Mar 20

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Mar 20

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Mar 20

1:30pm - Vincent Hall 364

Fri Mar 20

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
LECTURE CANCELED
Julie Thompson, Boston Scientific
Fri Mar 20

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Mar 20

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar - Cancelled

Thu Mar 19

Colloquium

3:35pm - Vincent Hall 16
Cancelled - Multiscale Geometric Methods for high-dimensional data near > low-dimensional sets
Colloquium Cancelled
Thu Mar 19

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Mar 19

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Mar 19

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed Mar 18

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory - Cancelled
Seminar Cancelled
Wed Mar 18

PDE Seminar

3:35pm - Vincent Hall 570 ,
PDE Seminar - Cancelled
Seminar Cancelled
Tue Mar 17

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 17

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Mar 17

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Mar 17

IMA Data Science Lab Seminar

1:25pm - Lind 305
CANCELED--Learning and Geometry for Stochastic Dynamical Systems in High Dimensions
-, -
Abstract:

We discuss geometry-based statistical learning techniques for performing model reduction and modeling of certain classes of stochastic high-dimensional dynamical systems. We consider two complementary settings. In the first one, we are given long trajectories of a system, e.g. from molecular dynamics, and we estimate, in a robust fashion, an effective number of degrees of freedom of the system, which may vary in the state space of then system, and a local scale where the dynamics is well-approximated by a reduced dynamics with a small number of degrees of freedom. We then use these ideas to produce an approximation to the generator of the system and obtain, via eigenfunctions of an empirical Fokker-Planck equation (constructed from data), reaction coordinates for the system that capture the large time behavior of the dynamics. We present various examples from molecular dynamics illustrating these ideas.

In the second setting we only have access to a (large number of expensive) simulators that can return short paths of the stochastic system, and introduce a statistical learning framework for estimating local approximations to the system, that can be (automatically) pieced together to form a fast global reduced model for the system, called ATLAS. ATLAS is guaranteed to be accurate (in the sense of producing stochastic paths whose distribution is close to that of paths generated by the original system) not only at small time scales, but also at large time scales, under suitable assumptions on the dynamics. We discuss applications to homogenization of rough diffusions in low and high dimensions, as well as relatively simple systems with separations of time scales, and deterministic chaotic systems in high-dimensions, that are well-approximated by effective stochastic diffusion-like equations.

Tue Mar 17

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Mar 16

Applied and Computational Math Colloquium

3:35pm - TBA
Applied and Computational Math Colloquium
Mauro Maggioni, Johns Hopkins
Mon Mar 16

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium - Cancelled
Colloquium Cancelled
Mon Mar 16

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Mar 16

Analysis and PDE Working Seminar

3:35pm - Vincent Hall 6
Analysis and PDE Working Seminar - Rescheduled for March 27

Mon Mar 16

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Mar 16

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Mar 16

Topology Seminar

2:30pm - VinH 364
Topology Seminar - TBA
Marcy Robertson, University of Melbourne

TBA

Mon Mar 16

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Mar 13

Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar
No Seminar - Spring Break
Fri Mar 13

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Mar 13

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Mar 13

1:30pm - Vincent Hall 364

Fri Mar 13

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Mar 13

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
No Seminar
Thu Mar 12

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Mar 12

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Mar 12

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Symplectic Topology

Wed Mar 11

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Tue Mar 10

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 10

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Mar 10

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Mar 10

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Mar 09

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Mar 09

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Mar 09

Analysis and PDE Working Seminar

3:35pm - Vincent Hall 6
Analysis & PDE Working Seminar

Mon Mar 09

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Mar 09

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Mar 09

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Mar 06

Combinatorics Seminar

3:35pm - Vincent Hall 570
Grothendieck Polynomials from Chromatic Lattice Models
Katy Weber
Abstract:

The -Grothendieck polynomials are simultaneous generalizations of Schubert and Grothendieck polynomials that arise in the study of the connective K-theory of the flag variety. They can be calculated as a generating function of combinatorial objects known as pipe dreams, as well as recursively via geometrically-motivated divided difference operators. We combine these two points of view by defining a chromatic lattice model whose partition function is a -Grothendieck polynomial. This is joint work-in-progress with Ben Brubaker, Claire Frechette, Andy Hardt, and Emily Tibor.

Fri Mar 06

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Mar 06

Probability Seminar

2:30pm - Vincent Hall 213
Dynamics of Deep Neural Networks and Neural Tangent Hierarchy
Jiaoyang Huang, Institute for Advanced Study
Abstract:

The evolution of a deep neural network trained by the gradient descent can be described by its neural tangent kernel (NTK) as introduced by Jacot et al., where it was proven that in the infinite width limit the NTK converges to an explicit limiting kernel and it stays constant during training. The NTK was also implicit in many other recent papers. In the overparametrization regime, a fully-trained deep neural network is indeed equivalent to the kernel regression predictor using the limiting NTK. And the gradient descent achieves zero training loss for a deep overparameterized neural network. However, it was observed by Arora et al. that there is a performance gap between the kernel regression using the limiting NTK and the deep neural networks. This performance gap is likely to originate from the change of the NTK along training due to the finite width effect.  The change of the NTK along the training is central to describe the generalization features of deep neural networks.In the work, we study the dynamic of the NTK for finite width deep fully-connected neural networks. We derive an infinite hierarchy of ordinary differential equations, the neural tangent hierarchy (NTH) which captures the gradient descent dynamic of the deep neural network. Moreover, under certain conditions on the neural network width and the data set dimension, we prove that the truncated hierarchy of NTH approximates the dynamic of the NTK up to arbitrary precision. This is a joint work with Horng-Tzer Yau.

Fri Mar 06

1:30pm - Vincent Hall 364

Fri Mar 06

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Mar 06

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
No Seminar
Thu Mar 05

Colloquium

3:35pm - Vincent Hall 16
Cluster formation and self-assembly in stratified fluids: a novel mechanism for particulate aggregation
Richard McLaughlin, UNC, Chapel HIll
Abstract:

The experimental and mathematical study of the motion of bodies immersed in fluids with variable concentration fields (e.g. temperature or salinity) is a problem of great interest in many applications, including delivery of chemicals in laminar micro-channels, or in the distribution
of matter in the ocean. In this lecture we present some recent experimental and mathematical advances we have made for several such problems. First, we review results on how the shape of a tube can be used to sculpt the profile of chemical delivery in pressure driven laminar shear flows. Then, we explore recent results for the behavior of matter trapped vertically in a variable density water column. For this second problem, we experimentally observe and mathematically model a new attractive mechanism we have found in our laboratory by which particles suspended within stratification may self-assemble and form large aggregates without need for short range binding effects (adhesion). This phenomenon arises through a complex interplay involving solute diffusion, impermeable boundaries, and the geometry of the aggregate, which produces toroidal flows. We show that these flows yield attractive horizontal forces between particles. We experimentally observe that many particles demonstrate a collective motion revealing a system which self-assembles, appearing to solve jigsaw-like puzzles on its way to organizing into a large scale disc-like shape, with the effective force increasing as the collective disc radius grows. We overview our modeling and simulation campaign towards understanding this intriguing dynamics,
which may play an important role in the formation of particle clusters in lakes and oceans.

Thu Mar 05

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Thu Mar 05

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
An invitation to contact homology
Erkao Bao, Scientist at the company Houzz in Palo Alto
Abstract:

Contact homology is an invariant of the contact structure, which is an odd-dimensional counterpart of a symplectic structure. It was proposed by Eliashberg, Givental and Hofer in 2000. The application of contact homology and its variants include distinguishing contact structures, knot invariants, the Weinstein conjecture and generalization, and calculating Gromov-Witten invariants. In this talk, I will start with the notion of contact structures, then give a heuristic definition of the contact homology as an infinite dimensional Morse homology, and finally explain the major difficulties to make the definition rigorous. This is a joint work with Ko Honda.

Wed Mar 04

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Tue Mar 03

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 03

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Mar 03

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Mar 03

IMA Data Science Lab Seminar

1:25pm - Lind 305
Living 3D World Models Leveraging Crowd Sourced Data
Abstract:

Crowd sourced imagery (images and video) is the richest data source available for 3D reconstruction of the world. The tremendous amounts of available imagery provided by photo/video sharing web sites, not only covers the worlds appearance, but also reflects the temporal evolution of the world, and its dynamic parts. It has long been a goal of computer vision to obtain life like virtual models from such rich imagery. The major current research challenges are the scale of the data, e.g. the Yahoo 100 million-image dataset (only presents a small fraction of what is needed to model our world), the diversity of data modalities (e.g. crowdsourced photos or satellite images), the robustness, the completeness of the registration, and the lack of data for dynamic elements. Specifically, we are currently facing significant challenges to process Internet scale crowd sourced imagery within a reasonable time frame given limited compute resources. This is particularly true as we move toward automatically creating content for virtual and augmented reality. The talk discusses the UNC groups work on highly efficient image registration for the reconstruction of static 3D models from world-scale photo collections on a single PC in the span of six days, as well as the groups related work on image-based search to address the scalability. It will also discuss the efforts to overcome the challenges achieving registration completeness and robustness. Additionally, the groups work towards overcoming the lack of observations for the reconstruction of scene dynamics will be presented. This includes for example, reconstructing people and fountains, using crowd-sourced Flickr imagery and videos to achieve the goal of bringing the 3D models to life will be presented.

Jan-Michael Frahm is a research scientist manager at Facebook and a full professor at the University of North Carolina at Chapel Hill where he heads the 3D computer vision group. He received his Dr.-Ing. in computer vision in 2005 from the Christian-Albrechts University of Kiel, Germany. His dissertation, Camera Self-Calibration with Known Camera Orientation received the prize for the best Ph.D. dissertation of the year in CAUs College of Engineering. His Diploma in Computer Science is from the University of Lübeck. His research interests include a variety of topics on the intersection of computer vision, computer graphics, AR & VR, and robotics. He has over 100 peer-reviewed publications, is a program chair f

Tue Mar 03

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Mar 02

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Mar 02

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Equilibration of aggregation-diffusion equations with weak interaction forces
Ruiwen Shu, University of Maryland
Abstract:

I will talk about the large time behavior of aggregation-diffusion equations. For one spatial dimension with certain assumptions on the interaction potential, the diffusion index $m$, and the initial data, we prove the convergence to the unique steady state as time goes to infinity (equilibration), with an explicit algebraic rate. The proof is based on a uniform-in-time bound on the first moment of the density distribution, combined with an energy dissipation rate estimate. This is the first result on the equilibration of aggregation-diffusion equations for a general class of weakly confining potentials $W(r)$: those satisfying $\lim_{r\rightarrow\infty}W(r)<\infty$.

Mon Mar 02

Analysis and PDE Working Seminar

3:35pm - Vincent Hall 6
Analysis & PDE Working Seminar

Mon Mar 02

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Mar 02

Student Number Theory Seminar

3:25pm - Vincent Hall 570
The Satake equivalence II: The geometric formulation
John O'Brien
Abstract:

We continue our discussion of the Satake equivalence and Langlands dual groups with an introduction to the geometric Satake equivalence. The classical Satake isomorphism establishes an algebra isomorphism between the spherical Hecke algebra of one group G and the Grothendieck group of the category of representations of the dual. We wish for a stronger statement--an equivalence of categories between a categorical analogue of the spherical Hecke algebra of G and the category of representations of the dual of G. The geometric Satake isomorphism establishes this equivalence, using the geometry of the affine Grassmannian of G to construct a suitable "spherical Hecke category" of G. In this talk, we discuss the affine Grassmannian and introduce the tools needed to understand the geometric Satake equivalence.

Mon Mar 02

Topology Seminar

2:30pm - VinH 364
Topology Seminar - TBA
George Shabat, Russian State University for the Humanities

TBA

Mon Mar 02

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Feb 28

MCFAM Seminar

5:30pm - Vincent Hall 16
Environmental, Social and Governance (ESG) in Finance Through the Lens of a Quant
Michael (Zicong) Zhang, Bloomberg LP
Abstract:

If you can't measure it, you can't manage it - Using math tricks in measuring ESG performance.
We will look at the science of scoring, focusing on quant techniques that enable investors to make choices based on meaningful ESG data.

Fri Feb 28

Combinatorics Seminar

3:35pm - Vincent Hall 570
Generalized snake graphs from orbifolds
Elizabeth Kelley
Abstract:

Cluster algebras, as originally defined by Fomin and Zelevinsky, are characterized by binomial exchange relations. A natural generalization of cluster algebras, due to Chekhov and Shapiro, allows the exchange relations to have arbitrarily many terms. A subset of these generalized cluster algebras can be associated with triangulations of orbifolds, analogous to the subset of ordinary cluster algebras associated with triangulated surfaces. We generalize Musiker-Schiffler-Williams snake graph construction for this subset of generalized cluster algebras, yielding explicit combinatorial formulas for the cluster variables. We then show that our construction can be extended to give expansions for generalized arcs on triangulated orbifolds. This is joint work with Esther Banaian.

Fri Feb 28

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Feb 28

Probability Seminar

2:30pm - Vincent Hall 213
Complexity of high dimensional Gaussian random fields with isotropic increments
Qiang Zeng, CUNY
Abstract:

The number of critical points (on the exponential scale) of a random function is a basic question and is commonly called complexity. The notion of locally isotropic random fields (a.k.a. random fields with isotropic increments) was introduced by Kolmogorov in the 1940s. Gaussian random fields on N-dimensional Euclidean spaces with isotropic increments were classified as isotropic case and non-isotropic case by Yaglom in the 1950s. In 2004, Fyodorov computed the large N limit (on the exponential scale) of expected number of critical points for isotropic Gaussian random fields. However, many natural models are not isotropic and only have isotropic increments, which creates new difficulty in understanding the complexity. In this talk, I will present some results on the large N behavior of complexity of non-isotropic Gaussian random fields with isotropic increments. Connection to random matrices will be explained. This talk is based on joint work with Antonio Auffinger (Northwestern University).

Fri Feb 28

1:30pm - Vincent Hall 364

Fri Feb 28

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Some Characteristics of Research in Finance
Onur Ozyesil, Helm.ai
Abstract:

The talk will provide a "naive" depiction of general characteristics of research in finance, together with an attempt to classify various research problems/styles present, in order to give a rough understanding of the landscape of mathematical research in finance. Two examples of research problems will also be discussed to provide a more concrete picture of research problems of interest in the industry.

Fri Feb 28

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Feb 28

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
$\tau$-Factorization and $\tau$-Elasticity
Bethany Kubik, University of Minnesota, Duluth
Abstract:

A more generalized form of factorization, called $\tau$-factorization, was introduced in 2011 by D.D. Anderson and J. Reinkoester. In $\tau$-factorization, all factors of a factorization must belong to the same equivalence class modulo a fixed ideal. We discuss $\tau$-factorization in small settings and $\tau$-elasticity in a more general setting.

Thu Feb 27

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Feb 27

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Wed Feb 26

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Wed Feb 26

Analysis and PDE Working Seminar

3:35pm - Vincent Hall 570
Local stability of the critical Fisher-KPP front via resolvent expansions near the essential spectrum
Montie Avery
Abstract:

We revisit the stability of the critical front in the Fisher-KPP equation, which travels with the linear spreading speed c = 2. We recover a celebrated result of Gallay with a new method, establishing stability of the critical front with optimal decay rate t^(-3/2) as well as an asymptotic description of the perturbation of the front. Our approach is based on studying detailed regularity properties of the resolvent for this problem in algebraically weighted spaces near the branch point in the absolute spectrum, and renders the nonlinear analysis much simpler. We briefly further explore the relationship between the localization of perturbations and their decay rate.

Tue Feb 25

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Feb 25

Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Feb 25

Dynamical Systems

2:30pm - Vincent Hall 213
Hyperbolic scattering in the N-body problem
Rick Moeckel, University of Minnesota
Abstract:

It is a classical result that in the N-body problem with positive energy, all solutions are unbounded in both forward and backward time. If all of the mutual distances between the particles tend to infinity with nonzero speed, the solution in called purely hyperbolic. In this case there is a well-defined asymptotic shape of the configuration of N points. We consider the scattering problem for solutions which are purely hyperbolic in both forward and backward time: given an initial shape at time minus infinity, which final shapes at time plus infinity can be reached via purely hyperbolic motions ? I will describe some recent work on this problem using a variation on McGehee's blow-up technique. After a change of coordinates and timescale we obtain a well-defined limiting flow at infinity and use it to get Chazy-type asymptotic estimates on the positions of the bodies and to study scattering solutions near infinity. This is joint work with G. Yu, R. Montgomery and N. Duignan.

Tue Feb 25

IMA Data Science Lab Seminar

1:25pm - Lind 305
Making Small Spaces Feel Large: Practical Illusions in Virtual Reality
Evan Rosenberg, University of Minnesota, Twin Cities
Abstract:

Over the next decade, immersive technologies have the potential to revolutionize how people communicate over distance, how they learn, train, and operate in challenging physical environments, and how they visualize, understand, and make decisions based on an ever-growing landscape of complex data. However, despite rapid technical advances over the past few years and no small amount of media hype, there are numerous theoretical and practical problems yet to be solved before virtual reality can catch up with our imaginations and make good on these promises. Locomotion is one of the most significant interaction challenges because body movement is constrained by the real world. When walking in VR, users may collide with walls or physical obstacles if they attempt to travel outside the boundaries of a "room-scale" space. In this talk, I will present a series of illusory techniques that can overcome these movement limitations by imperceptibly manipulating the laws of physics. This approach, known as redirected walking, has stunning potential to fool the senses. Through a series of formal studies, users have been convinced that were walking along a straight path while actually traveling in a circle, or that they were exploring impossibly large virtual environments within the footprint of a single real-world room. Additionally, I will discuss technical challenges for redirected walking systems and present novel algorithms that can automatically redirect users in complex physical spaces with obstacles.

Evan Suma Rosenberg is an Assistant Professor in the Department of Computer Science and Engineering at the University of Minnesota. Previously, he was the Associate Director of the MxR Lab at the Institute for Creative Technologies and a Research Assistant Professor in the Department of Computer Science at the University of Southern California. His research interests are situated at the intersection of virtual/augmented reality and HCI, encompassing immersive technologies, 3D user interfaces, and spatial interaction techniques. He received his Ph.D. from the Department of Computer Science at the University of North Carolina at Charlotte in 2010. Dr. Suma Rosenberg's research has been recognized with multiple best paper awards and has been funded by NSF, ARL, ONR, and DARPA. Over the past decade, he has also directed the development of multiple publicly released free software projects and contributed to an open-source technology initiative that has had a majo

Tue Feb 25

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Feb 24

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium - Canceled
Canceled
Mon Feb 24

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Feb 24

Student Number Theory Seminar

3:35pm - Vincent Hall 570
The Satake equivalence I: The classical formulation
John O'Brien
Abstract:

When studying the representation theory of reductive groups, one runs into a mysterious phenomenon: a certain duality between certain groups. In 1963, Ichir? Satake gave one of the first attempts of
explaining this duality--the Satake isomorphism between the spherical Hecke algebra of one group over a local field with the complexified representation ring of the Langlands dual group. In this duo of talks,
we will discuss two formulations of the Satake equivalence: the classical formulation in terms of algebras, and the more recent geometric formulation in terms of categories related to the affine Grassmannian, an infinite-dimensional space. For this first talk, we will give an overview of the classical formulation.

Mon Feb 24

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Feb 24

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Feb 21

MCFAM Seminar

5:30pm - VinH 16
2020 Winter FM Modeling Workshop Presentations
2020 Financial Mathematics (FM) Modeling Workshop Graduate Students, University of Minnesota
Abstract:

Two teams of Financial Mathematics graduate students will present the results of their projects completed over an intensive 10-day winter workshop.  The first presentation will be on Data Analysis, Visualization and Statistical/Machine Learning Modeling for Mortgage Prepayment and Delinquency Rates. The Industry Mentor for this project , in attendance for the talk, was: He LuThe second presentation will be on Inflation Rate Curve Modeling.  This project was led by Industry Mentor Matt Abroe.

Fri Feb 21

Combinatorics Seminar

3:35pm - Vincent Hall 570
Separable elements and splittings of Weyl groups
Yibo Gao, MIT
Abstract:

We introduce separable elements in finite Weyl groups, generalizing the well-studied class of separable permutations. They enjoy nice properties in the weak Bruhat order, enumerate faces of the graph associahedron of the corresponding Dynkin diagrams, and can be characterized by pattern avoidance in the sense of Billey and Postnikov. We then prove that the multiplication map W/V×V?WW/V×V?W for a generalized quotient of the symmetric group is always surjective when V is a principal order ideal, providing the first combinatorial proof of an inequality due originally to Sidorenko in 1991, answering an open problem of Morales, Pak, and Panova. We show that this multiplication map is a bijection if and only if V is an order ideal in the right weak order generated by a separable element, answering an open question of Björner and Wachs in 1988. This is joint work with Christian Gaetz.

Fri Feb 21

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Feb 21

Probability Seminar

2:30pm - Vincent Hall 213
Robust Representation for Graph Data
Dongmian Zou, UMN
Abstract:

Modern data are usually high-dimensional with noise and corruption. A useful representation of data has to be robust and address the data structure. In this talk, I will first present a class of robust models called the scattering transform that can be used to generated features from graph data. In graph scattering transforms, the representation is generated in an unsupervised manner based on graph wavelets. It is approximately invariant to permutations and stable to signal or graph manipulations. Numerical results show that it works effectively for classification and community detection problems. Next, I will address how the structure of data can be found using autoencoders. Indeed, in the framework of autoencoders, graph scattering transform can be applied to the important task of graph generation. Specifically, I will illustrate its application in generating molecular samples.

Fri Feb 21

1:30pm - Vincent Hall 364

Fri Feb 21

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Profiles of Math Careers in the Industry
Martin Lacasse, ExxonMobil
Abstract:

While the majority of PhD students graduating in math and physics end up being employed by the industry, there is relatively little information of career opportunities in the industry being presented to students during their graduate studies. This presentation aims at providing some real examples of career paths for mathematicians in the industry, and describing specific problems being addressed by them. The talk is intended to be an informal discussion around how to better prepare oneself to address the challenges raised by pursuing a career in the industry.

A French-Canadian native, Martin Lacasse completed undergraduate degrees in both chemistry (Montreal) and physics (Concordia) where he graduated first of his promotion. He then studied at McGill University where he earned a M.Sc. and a Ph.D. in Physics, studying problems in statistical mechanics related to critical phenomena and phase transitions using large-scale computers. After his Ph.D., Lacasse moved to Princeton University for a joint post-doctoral fellowship with the Corporate Research Laboratory (CSR) of Exxon Research and Engineering. Shortly after in 1995, he joined the lab and worked on the thermodynamics of polymer interfaces and on the rheology of compressed emulsions. Lacasse is currently leading a team of researchers at CSR modeling the effects of induced seismicity during oil and gas production. His current research interests also include experimental design problems in the field of PDE-constrained optimization and the packing of non-spherical particles. Over the years, Lacasse has been recognized as a leader in high-performance computing.

Fri Feb 21

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Feb 21

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Thu Feb 20

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Feb 20

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Wed Feb 19

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Tue Feb 18

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Feb 18

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Feb 18

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Feb 18

IMA Data Science Lab Seminar

1:25pm - Lind 305
From Clustering with Graph Cuts to Isoperimetric Inequalities: Quantitative Convergence Rates of Cheeger Cuts on Data Clouds
Nicolas Garcia Trillos, University of Wisconsin, Madison
Abstract:

Graph cuts have been studied for decades in the mathematics and computer science communities. For example, a celebrated result in optimization relates the cut minimization problem (under some membership constraints) with a maximum flow problem via the well known max flow-min cut duality theorem. Another very important problem formulated in the computer science community that uses graph cuts is motivated by data clustering: while direct minimization of a graph cut is reasonable as it penalizes the size of interfaces, the optimization is not able to rule out partitions of data into groups that are highly asymmetric in terms of size. In order to avoid trivial partitions, and provide a more reasonable clustering approach, the original optimization of graph cuts is modified by adding an extra balancing term to the objective function in either additive or multiplicative form. A canonical example, with historical motivation, is the so called Cheeger cut problem. Minimization of Cheeger cuts for data clustering is on the one hand intuitively motivated, but on the other, is a highly non-convex optimization problem with a pessimistic NP hard label tamped on it (at least in a worst case scenario setting). Nevertheless, in the past decade or so, several algorithmic improvements made the minimization of Cheeger cuts more feasible, and at the same time there was a renewed interest in studying statistical properties of Cheeger cuts. New analytical ideas have provided new tools to attack problems that were elusive using classical approaches from statistics and statistical learning theory. Despite the advances, several questions remain unanswered.

The purpose of this talk is to present some of these theoretical developments, with emphasis on new results where, for the first time, high probability converge rates of Cheeger cuts of proximity graphs over data clouds are deduced. These quantitative convergence rates are obtained by building bridges between the original clustering problem and another field within the mathematical analysis community that has seen enormous advancements in the past few years: quantitative isoperimetric inequalities. This connection serves as a metaphor for how the mathematical analyst may be able to contribute to answer theoretical questions in machine learning, and how one may be able to deduce statistical properties of solutions to learning optimization problems that have a continuum counterpart.

Tue Feb 18

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Feb 17

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Feb 17

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Direct Sampling Algoritmis in Inverse Scattering
Isaac Harris, Purdue University
Abstract:

In this talk, we will discuss a recent qualitative imaging method referred to as the Direct Sampling Method for inverse scattering. This method allows one to recover a scattering object by evaluating an imaging functional that is the inner-product of the far-field data and a known function. It can be shown that the imaging functional is strictly positive in the scatterer and decays as the sampling point moves away from the scatterer. The analysis uses the factorization of the far-field operator and the Funke-Hecke formula. This method can also be shown to be stable with respect to perturbations in the scattering data. We will discuss the inverse scattering problem for both acoustic and electromagnetic waves.

Mon Feb 17

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Feb 17

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Feb 17

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Feb 14

Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics of the double-dimer model
Helen Jenne, Oregon
Abstract:

In this talk we will discuss a new result about the double-dimer model: under certain conditions, the partition function for double-dimer configurations of a planar bipartite graph satisfies an elegant recurrence, related to the Desnanot-Jacobi identity from linear algebra. A similar identity for the number of dimer configurations (or perfect matchings) of a graph was established nearly 20 years ago by Kuo
and others. We will also explain one of the motivations for this work, which is a problem in Donaldson-Thomas and Pandharipande-Thomas theory that will be the subject of a forthcoming paper with Gautam Webb and Ben Young.

Fri Feb 14

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Feb 14

Probability Seminar

2:30pm - Vincent Hall 213
Order of Fluctuations of the Sherrington-Kirkpatrick Model at Critical Temperature
Wei-Kuo Chen, UMN
Abstract:

I will discuss the order of fluctuations in the Sherrington-Kirkpatrick mean field spin glass model. In particular, I will focus on the predictions concerning the free energy and present an elementary approach for obtaining a logarithmic bound on its variance at the critical temperature.

Fri Feb 14

1:30pm - Vincent Hall 364

Fri Feb 14

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Feb 14

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Tate Resolutions and Horrocks Splitting Criterion
&nbsp;Mahrud Sayrafi&nbsp;&nbsp;, &nbsp;
Abstract:

I will talk about the two papers Eisenbud-Fløystad-Schreyer-2003 and Eisenbud-Erman-Schreyer-2015 in which they introduce Tate resolutions for projective spaces and products of projective spaces. As an application, I will talk about Horrocks' criterion for vector bundles in those settings.

Thu Feb 13

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Feb 13

Special Events and Seminars

2:30pm - Vincent Hall 570
Vector Bundles on the Projective Space
Mahrud Sayrafi, University of Minnesota
Abstract:

I will start with the basics of line bundles and vector bundles in commutative algebra, specifically over the projective space. This is an introduction for the talk on Friday at the Commutative Algebra Seminar about the Tate resolutions for projective spaces and products of projective spaces.

Wed Feb 12

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Tue Feb 11

Colloquium

3:30pm - Vincent Hall 16
Understanding maps between Riemann surfaces
Felix Janda, Institute for Advanced Study in Princeton
Abstract:

Moduli spaces of Riemann surfaces are a fundamental object in algebraic geometry. Their geometry is rich and holds many outstanding mysteries. One way to probe genus g Riemann surfaces is to understand the maps they admit to the simplest Riemann surface, the Riemann sphere. In my talk, I will describe one facet of this approach, a formula for the double ramification cycle (joint work with R. Pandharipande, A. Pixton and D. Zvonkine). Along the way, we will see connections to combinatorics, number theory and symplectic geometry.

Tue Feb 11

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Feb 11

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Feb 11

IMA Data Science Lab Seminar

1:25pm - Lind 305
Function Space Metropolis-Hastings Algorithms with Non-Gaussian Priors
Bamdad Hosseini, California Institute of Technology
Abstract:

Metropolis-Hastings (MH) algorithms are one of the most widely used methods for inference.
However, the convergence properties of these algorithms often deteriorate in high-dimensions
making them unsuitable for Bayesian inverse problems and non-parametric inference where,
in principle, the problem is defined on an infinite-dimensional Hilbert or Banach space.

In this talk we discuss some ideas for designing new MH algorithms that are reversible with
dimension-independent convergence properties. We present a new class of algorithms called
RCAR, that is tailored to priors based on the gamma distribution. We present an application of
RCAR for a deconvolution inverse problem and consider its convergence properties and consistent
approximation.

I am a von Karman instructor in the Department of Computing and Mathematical Sciences at California Institute of Technology, sponsored by Prof. Andrew Stuart. Prior to that I received my Ph.D. in Applied and Computational Mathematics in the Department of Mathematics at Simon Fraser University with of Profs. Nilima Nigam and John Stockie. I work on problems at the interface of probability, statistics and applied mathematics with a particular focus on the analysis, development and application of computational methods for estimating parameters and quantifying uncertainty.

Tue Feb 11

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Feb 10

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Feb 10

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Feb 10

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Feb 10

Student Number Theory Seminar

3:25pm - Vincent Hall 570
The Conditional Probability That an Elliptic Curve Has a Rational Subgroup of Order 5 or 7
Meagan Kenney
Abstract:

Let E be an elliptic curve over the rationals. Divisibility of the set of rational points on E by some integer m can occur locally or globally. If E has global divisibility by m, then E has local divisibility by m; however, work of Katz shows that the converse is only guaranteed up to isogeny. Cullinan and Voight showed that the probability than an elliptic curve has global divisibility by an integer m is non-zero for all integers m allowed by Mazur's classification of rational torsion on elliptic curves. In this talk, I will discuss the probability that E has global divisibility by 5 or 7, given that E has local divisibility by 5 or 7, respectively.

Mon Feb 10

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Feb 07

MCFAM Seminar

5:30pm - Vincent Hall 16
Pricing in Contractual Freight Compared to Finance
Kaisa Taipale, C.H. Robinson
Abstract:

In this talk, I'll discuss the contractual freight business, in which a large shipper makes a contract with a company like CH Robinson to procure carriers (trucks) for their goods over the course of a year for a given rate, as opposed to using the volatile "spot" or transactional market. Because these year-long contracts aren't legally binding, some shippers treat them more like an American option on the underlying price of freight, but this has game-theoretic economic consequences for the shipper! Dr. Taipale, Data Scientist at C.H. Robinson will also talk about the data science and mathematical skills that are important for her job at C.H. Robinson

Fri Feb 07

Combinatorics Seminar

3:35pm - Vincent Hall 570
Unconditional Reflexive Polytopes
McCabe Olsen, Ohio State
Abstract:

A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this paper, we investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study the signed Birkhoff polytope. Moreover, we derive constructions for Gale-dual pairs of polytopes and we explicitly describe Gröbner bases for unconditional reflexive polytopes coming from partially ordered sets. This is joint work with Florian Kohl (Aalto University) and Raman Sanyal (Goethe Universität Frankfurt).

Fri Feb 07

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Feb 07

Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Feb 07

1:30pm - Vincent Hall 364

Fri Feb 07

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Feb 07

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
On a question of Dutta, joint with Linquan Ma and Anurag Singh
Uli Walther, Purdue
Abstract:

For a local ring (A,m) of dimension n,we study the natural map from the n-th Koszul cohomology on a minimal set of generators of m to the top local cohomology of A supported at m. We construct complete normal domains for which this map is zero, thus answering a question of Dutta in the negative. If time permits, we present precise information on the kernel of this map for a large class of Stanley-Reisner rings.

Thu Feb 06

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Feb 06

Special Events and Seminars

2:30pm - Vincent Hall 570
Student Commutative Algebra Seminar

Wed Feb 05

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Tue Feb 04

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Feb 04

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Feb 04

Dynamical Systems

2:30pm - Vincent Hall 213
Spectral Stability, the Maslov Index, and Spatial Dynamics
Margaret Beck, Boston University
Abstract:

Understanding the spectral stability of solutions to partial differential equations is an important step in predicting long-time dynamics. Recently, it has been shown that a topological invariant known as the Maslov Index can play an important role in determining spectral stability for systems that have a symplectic structure. In addition, related ideas have lead to a suggested generalization of the notion of spatial dynamics to general, multidimensional spatial domains. In this talk, the notions of spectral stability, the Maslov Index, and spatial dynamics will be introduced and an overview of recent results will be given.

Tue Feb 04

IMA Data Science Lab Seminar

1:25pm - Lind 305
Different Aspects of Registration Problem
Yuehaw Khoo, University of Chicago
Abstract:

In this talk, we discuss several variants of the rigid registration problem, i.e aligning objects via rigid transformation. In the simplest scenario of point-set registration where the correspondence between points are known, we investigate the robustness of registration to outliers. We also study a convex programming formulation of point-set registration with exact recovery, in the situation where both the correspondence and alignment are unknowns. Lastly, an important registration problem arises in Cryo-electron microscopy for protein structuring will be discussed. This talk is based on joint works with Ankur Kapoor, Joe Kileel, Boris Landa, Cindy Orozco, Amit Singer, Nir Sharon, and Lexing Ying.

Yuehaw Khoo is an assistant professor in the statistics department of University of Chicago. Prior to this, he was a post-doc in Stanford and graduate student in Princeton. He is interested in scientific computing problems in protein structure determination and quantum many-body physics. In these problems, he focuses on non-convex, discrete or large scale optimization and representing high-dimensional functions using neural-network and tensor network.

Tue Feb 04

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Feb 03

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
On the final frontiers in computational mathematics
Anders Hansen, Cambridge
Abstract:

Core problems in computational mathematics include computing spectra of operators, solutions to linear PDEs, convex optimisation problems etc., and these areas have been intensely investigated over the last half century. However, there are still fundamental open problems. For example, despite more than 90 years of quantum mechanics, it is still unknown whether it is possible to compute spectra of Schrodinger operators with bounded potentials. Moreover, how to compute minimisers of linear programs (LP) with rational inputs has been known since the 1950s, however, what happens if the input is irrational? Can one accurately compute minimisers of LPs if, as in compressed sensing, the matrix has rows from the discrete cosine transform? Furthermore, do there exist algorithms that can handle all linear Schrodinger PDEs? And, if not, which can be handled and which can never be solved? We will discuss solutions to many of these open problems and provide some potentially surprising results. For example, despite being open for decades, the problem of computing spectra of Schrodinger operators with bounded potentials is not harder than computing spectra of diagonal infinite matrices, the easiest of computational spectral problems. Moreover, for LPs with irrational inputs we have the following phenomenon. For any integer K > 2 there exists a class of well conditioned inputs so that no algorithm can compute K correct digits of a minimiser, however, there exists an algorithm that can compute K-1 correct digits. But any algorithm producing K-1 correct digits will need arbitrarily long time. Finally, computing K-2 correct digits can be done in polynomial time in the number of variables.

Mon Feb 03

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
Applied and Computational Mathematics Seminar

Mon Feb 03

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Feb 03

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Paul Garrett
Abstract:

One hundred years ago, when the theory of self-adjoint operators was
just being developed, Hilbert and Polya independently speculated on
the possibility of using self-adjoint operators (the fact that all
eigenvalues are real) to prove the Riemann Hypothesis. In 1977, a
flawed numerical computation of eigenvalues of the invariant
Laplace-Beltrami operator on the modular curve seemed to indicate that
zeros of zeta appeared as spectral parameters.

Mon Feb 03

Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Fri Jan 31

Combinatorics Seminar

3:35pm - Vincent Hall 570
Weak order and descents for monotone triangles
Vic Reiner
Abstract:

(joint work with Zach Hamaker; arXiv:1809.1057) Monotone triangles are combinatorial objects in bijection with alternating sign matrices, a fascinating generalization of permutation matrices. We will review this connection, and the fact that strong Bruhat order on permutations has a natural extension to monotone triangles. We will then explain an analogous extension of the weak Bruhat order on permutations to monotone triangles. This comes from extending the notions of descents in permutations and the "bubble-sorting" action of the 0-Hecke algebra on permutations to monotone triangles. We will also explain one of our motivations: to give a natural family of shellings for Terwilliger's recently defined order on subsets.

Fri Jan 31

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Jan 31

Probability Seminar

2:30pm - Vincent Hall 213
Near-critical avalanches in 2D frozen percolation and forest fires
Wai-Kit Lam, UMN
Abstract:

We consider (volume-)frozen percolation on the triangular lattice. The model can be described informally as follows. Fix a large integer $N$. Initially, all vertices are vacant. We let clusters grow (vertices become occupied) as long as their volume is strictly smaller than $N$, and they stop growing (they "freeze") when their volume becomes at least $N$. A vertex $v$ is frozen if it belongs to an occupied cluster with volume at least $N$.

In this model, there exists a sequence of "exceptional scales" $(m_k(N))$: roughly speaking, if we consider frozen percolation in a box of side length $m_k(N)$, then as $N\to\infty$, the probability that $0$ is frozen in the final configuration is bounded away from $0$; while if we consider the process in a box of side length that is far from $m_k(N)$ and $m_{k+1}(N)$ (but between them), then as $N\to\infty$, the corresponding probability will go to $0$. The limiting exception scale, $m_\infty(N)$, is not studied and almost nothing is known. In an ongoing project with Pierre Nolin, we show that if we consider the process in a box of side length $m_\infty(N)$, then there are "avalanches" of freezings: the number of frozen circuits surrounding the origin divided by $\log\log{N}$ converges to an explicit constant in probability. If time allows, I will also talk about the analogous result in the forest fire process.

Fri Jan 31

1:30pm - Vincent Hall 364

Fri Jan 31

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
How NextEra Analytics Applies Math to Problems in Coupled Renewable and Energy Storage Systems
Abstract:

Renewable energy sources - solar and wind - are inherently variable, and unlike a traditional power plant, energy generation can't be 'turned up' or 'turned down' at will. In the past several years, the rapidly falling price of Lithium Ion batteries and related technology has made it more feasible than ever to build solar or wind farms coupled with energy storage capabilities to mitigate some of the variability of the renewable resource and provide more control over the energy output of the farm. In this talk, I will give an overview of working at NextEra Analytics and give examples of how we are applying math to operate energy storage projects as well as evaluate potential new renewable + energy storage hybrid projects.

Madeline graduated in May from the University of Minnesota with a PhD in Mathematics co-advised by Drs. Gilad Lerman and Wei-Kuo Chen. She started in the Applied Math Group at NextEra Analytics in June and works primarily on math related to energy storage.

Fri Jan 31

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Jan 31

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar

Thu Jan 30

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Wed Jan 29

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Tue Jan 28

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Jan 28

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Jan 28

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Jan 28

IMA Data Science Lab Seminar

1:25pm - Lind 409
Machine Learning Meets Societal Values
Steven Wu, University of Minnesota, Twin Cities
Abstract:

The vast collection of detailed personal data has enabled machine learning to have a tremendous impact on society. Algorithms now provide predictions and insights that are used to make or inform consequential decisions on people. Concerns have been raised that our heavy reliance on personal data and machine learning might compromise peoples privacy, produce new forms of discrimination, and violate other kinds of social norms. My research seeks to address this emerging tension between machine learning and society by focusing on two interconnected questions: 1) how to make machine learning better aligned with societal values, especially privacy and fairness, and 2) how to make machine learning methods more reliable and robust in social and economic dynamics. In this talk, I will provide an overview of my research and highlight some of my recent work on fairness in machine learning and differentially private synthetic data generation.

Steven Wu is an Assistant Professor of Computer Science and Engineering at the University of Minnesota. His research interests are in algorithms and machine learning, with a focus on privacy-preserving data analysis, algorithmic fairness, and algorithmic economics. From 2017 to 2018, he was a post-doc researcher at Microsoft Research-New York City in the Machine Learning and Algorithmic Economics groups. In 2017, he received his Ph.D. in computer science under the supervision of Michael Kearns and Aaron Roth at the University of Pennsylvania, where his doctoral dissertation received Penns Morris and Dorothy Rubinoff Award for best thesis. His research is supported by an Amazon Research Award, a Facebook Research Award, a Mozilla research grant, a Google Faculty Research Award, a J.P. Morgan Research Faculty Award, and the National Science Foundation.

Tue Jan 28

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Jan 27

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Jan 27

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 311
An inverse problem on Light Sheet Fluorescence Microscopy
Benjamin Palacios, University of Chicago
Abstract:

In Light Sheet Fluorescence Microscopy a density of fluorescent material (fluorophores) needs to be reconstructed through a process that consists in the application of a thin sheet of light that stimulates fluorophores, inducing the emission of fluorescent light that is recorderded and which constitute our measurements. In this talk I will present a mathematical model for this two-step process as well as the inverse problem arising from it. Uniqueness and stability of the inverse problem will be discussed.

Mon Jan 27

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jan 27

Student Number Theory Seminar

3:25pm - Vincent Hall 570
Student Number Theory Seminar

Mon Jan 27

Topology Seminar

2:30pm - Vincent Hall 311
Smooth 4-manifolds and the geometry of 3-manifolds
Matthew Stoffregen, MIT
Abstract:

One of the interests of low-dimensional topologists is
understanding which smooth 4-manifolds can bound a given 3-manifold, or,
as a special case, understanding the set of 3-manifolds up to so-called
homology cobordism (to be defined in the talk). This question turns out
to have applications to the study of triangulations of high-dimensional
manifolds, and is a natural proving ground for Floer-theoretic
techniques of studying 3-manifolds. In this talk, we will give some
structure theorems about the homology cobordism group, and show that
there are three-manifolds that are very far from having any of the seven
non-hyperbolic Thurston geometries. This talk includes joint work with
I. Dai, K. Hendricks, J. Hom, L. Truong, and I. Zemke.

Fri Jan 24

MCFAM Seminar

5:30pm - Vincent Hall 16
U of MN Women in Math and Stats Graduate Team - 2019 MinneMUDAC Award Winning Analytics Presentation on Commodity Pricing
Cora Brown, Somyi Baek, Sarah Milstein, and Yu Yang, University of Minnesota
Abstract:

University of Minnesota mathematics and statistics graduate students formed a team called "Women in Math and Stats" and competed in the MinneMUDAC 2019 Challenge. They took 2nd place in a field of 24 teams in the graduate division of the challenge. They also received the Analytic Acumen Award for the 2nd year in a row. This years challenge required students to analyze a variety of data to predict trends in soybean prices. Teams were evaluated based on a number of factors, including data preparation, team synergy, and communication of results. Teams in the Undergraduate and Graduate divisions were also scored on the accuracy of their predictions. The challenge and data were curated by Farm Femmes. We firmly believe that investing in the next generation grows the future, said Karen Hildebrand, Co-Founder of Farm Femmes. Some days the seeds we plant are literal as farmers, but MinneMUDAC gave us the opportunity to grow the knowledge of agriculture and agtech.Members of the team who will presenting include: Cora Brown, Somyi Baek, Sarah Milstein, and Yu Yang. Their faculty advisor was Dr. Gilad Lerman.

Fri Jan 24

Lie Theory Seminar

3:30pm - Vincent Hall 209
Lie Theory Seminar

Fri Jan 24

1:30pm - Vincent Hall 364

Fri Jan 24

Special Events and Seminars

1:00pm - Vincent Hall 301
p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions

Fri Jan 24

Commutative Algebra Seminar

12:20pm - VinH 203A
Commutative Algebra Seminar

Thu Jan 23

Colloquium

3:35pm - Vincent Hall 16
Modularity and the Hodge/Tate conjectures for some self-products
Laure Flapan, MIT
Abstract:

If X is a smooth projective variety over a number field, the Hodge and Tate conjectures describe how information about the subvarieties of X is encoded in the cohomology of X. We explore the role that certain automorphic representations, called algebraic Hecke characters, can play in understanding which cohomology classes of X arise from subvarieties. We use this to deduce the Hodge and Tate conjectures for certain self-products of varieties, including some self-products of K3 surfaces. This is joint work with J. Lang.

Wed Jan 22

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Tue Jan 21

Colloquium

3:30pm - Vincent Hall 16
Optimal Transport as a Tool in Analytic Number Theory and PDEs
Stefan Steinerberger, Yale University
Abstract:

Optimal Transport is concerned with the question of how to best move one measure to another (this could be sand on a beach or products from a warehouse to consumers). I will explain the basic definition of Wasserstein distance and then describe how it can be used as a tool to say interesting things in other fields. (1) How to get new regularity statements for classical objects in number theory almost for free (irrational rotations on the torus, quadratic residues in finite fields). (2) How to best distribute coffee shops over downtown Minneapolis. (3) Finally, how to obtain higher dimensional analogues of classical Sturm-Liouville theory: simply put, Sturm-Liouville theory says that eigenfunctions of the operator Ly = -y''(x) +p(x)y(x) (think of sin(kx) and cos(kx)) cannot have an arbitrary number of roots; we present a generalization to higher dimensions that is based on a simple (geometric) inequality.

Tue Jan 21

Special Events and Seminars

3:30pm - Vincent Hall 364
Arithmetic Geometry Seminar

Tue Jan 21

Dynamical Systems

2:30pm - Vincent Hall 213
Dynamical Systems Seminar

Tue Jan 21

IMA Data Science Lab Seminar

1:25pm - Lind 305
Linear Unbalanced Optimal Transport
Matthew Thorpe, University of Cambridge
Abstract:

Optimal transport is a powerful tool for measuring the distances between
signals. However, the most common choice is to use the Wasserstein
distance where one is required to treat the signal as a probability
measure. This places restrictive conditions on the signals and although
ad-hoc renormalisation can be applied to sets of unnormalised measures
this can often dampen features of the signal. The second disadvantage is
that despite recent advances, computing optimal transport distances for
large sets is still difficult. In this talk I will focus on the
Hellinger--Kantorovich distance, which can be applied between any pair
of non-negative measures. I will describe how the distance can be
linearised and embedded into a Euclidean space. The Euclidean distance
in the embedded space is approximately the Wasserstein distance in the
original space. This method, in particular, allows for the application
of off-the-shelf data analysis tools such as principal component
analysis.

This is joint work with Bernhard Schmitzer (TU Munich).

Matthew is a research fellow in the Cantab Capital Institute for the
Mathematics of Information at the University of Cambridge. Prior to that
he was a postdoctoral associate at Carnegie Mellon University and a PhD
student at the University of Warwick. From this coming March he will be
a lecturer (US equivalent Assistant Professor) in Applied Mathematics at
the University of Manchester.

Tue Jan 21

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Jan 20

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Tue Jan 14

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Jan 13

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Tue Jan 07

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Jan 06

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Tue Dec 31

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Dec 30

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Tue Dec 24

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Dec 23

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Dec 20

Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar

Fri Dec 20

1:30pm - Vincent Hall 1

Thu Dec 19

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Dec 19

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
TBA
Thu Dec 19

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Dec 18

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Dec 18

PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Tue Dec 17

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Dec 17

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Dec 17

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Dec 16

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Dec 16

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 16

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Dec 13

Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar
No Seminar - Final Exams
Fri Dec 13

Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Dec 13

1:30pm - Vincent Hall 1

Fri Dec 13

Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Thu Dec 12

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Dec 12

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Dec 12

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
TBA
Thu Dec 12

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar

Thu Dec 12

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Dec 11

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Dec 11

PDE Seminar

3:35pm - Vincent Hall 570
Quantitative stochastic homogenization via Malliavin calculus
Antoine Gloria, Sorbonne Université
Abstract:

Abstract: This talk is about stochastic homogenization of linear elliptic equations in divergence form. Let $a(x)=h(G(x))$ be a diffusion coefficient field, where $h$ is a Lipschitz function and $G$ is a Gaussian field (with possibly thick tail). Solutions $u_\varepsilon$ of elliptic equations $-\nabla \cdot a(\cdot/\varepsilon) \nabla u_\varepsilon = \nabla \cdot f$ in $\mathbb R^d$ with such random heterogeneous coefficients $a$ both oscillate spatially and fluctuate randomly at scale $\varepsilon >0$. I will show how suitable quantitative two-scale expansions allow one to reduce the analysis of oscillations and fluctuations of solutions to bounds on the corrector and fluctuations of the homogenization commutator, respectively. The main probabilistic ingredient is Malliavin calculus, and the main analytical ingredient is large-scale elliptic regularity. This is based on joint works with Mitia Duerinckx, Julian Fischer, Stefan Neukamm, and Felix Otto.

Wed Dec 11

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Dec 10

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Dec 10

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Dec 10

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Dec 10

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology Seminar
TBA
Tue Dec 10

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Dec 09

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Gradient Flows: From PDE to Data Analysis
Franca Hoffman, Caltech
Abstract:

Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.

Mon Dec 09

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Dec 09

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 09

Topology Seminar

2:30pm - Ford Hall 110
Topology Seminar
TBA
Mon Dec 09

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Dec 06

MCFAM Seminar

5:30pm - Vincent Hall 16
GUN VIOLENCE: ACTUARIAL ANALYSIS AND MATHEMATICAL MODELING
Kristen Moore, University of Michigan
Abstract:

Firearm deaths and injuries are a significant problem in the United States. Indeed, the American Medical Association recently called firearm violence a public health crisis and called for a comprehensive public health response and solution. Gun violence in America exacts a significant toll on our society in both human and economic terms. Some argue that Americans have a moral obligation to address the issue of gun violence. But even from a more concrete perspective, the economic cost of firearms directly impacts the financial outcomes of insurers and taxpayers. There is a clear need for unbiased and objective research on the societal and economic impact of firearms. Actuaries are well positioned to study the mortality and morbidity related to firearms, both to quantify the risk and to inform governmental and public health interventions to mitigate the risk associated with firearms. Yet there is little on the topic in the actuarial and insurance literature. In this talk, I will provide a brief overview on the scope of firearm deaths and injuries and examine the extent to which actuaries and insurance professionals have studied or addressed the issue. I will compare firearm risk to risks that are considered in the underwriting process for life and homeowners insurance. I will describe some existing insurance products related to firearm risk as well as proposed legislation regarding gun liability insurance. In a different vein, if time permits, I will discuss preliminary work on a dynamical systems model of gun violence within a population. We are studying how, in an idealized model, changes to various policy parameters affect the long-term behavior of a system. Finally, I will describe some of the many open questions related to gun violence that are amenable to study by actuaries and mathematicians. Bio: https://sites.lsa.umich.edu/ksmoore/

Fri Dec 06

Lie Theory Seminar

3:35pm - Vincent Hall 1
Special modular forms on exceptional groups
Aaron Pollack, Duke University
Abstract:

Classically, a Siegel modular form is said to be singular or distinguished if many of its Fourier coefficients are 0, in a precise sense. I will explain the construction of singular and distinguished modular forms on the exceptional groups E_6, E_7, E_8. Moreover, time permitting, I will also explain an analogue of the Saito-Kurokawa lift, which produces cusp forms on Spin(8) and the exceptional group G_2 out of holomorphic Siegel modular forms on Sp(4).

Fri Dec 06

Combinatorics Seminar

3:30pm - Vincent Hall 570
A non-iterative formula for straightening fillings of Young diagrams
Reuven Hodges, UIUC
Abstract:

Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. It has been a long-standing open problem to give a non-iterative formula for this straightening process. In this talk I will give such a formula. I will then use this non-iterative formula give a proof that the coefficient of the leading term in the straightening is either 1 or -1, generalizing a theorem of Gonciulea and Lakshmibai.

Fri Dec 06

Probability Seminar

2:30pm - Vincent Hall 311
Gibbsian line ensembles and log-gamma polymers
Xuan Wu, Columbia University
Abstract:

In this talk we will first give an overview of the known
Gibbsian line ensembles in the KPZ universality class. Then we will
construct the discrete log-gamma line ensemble, which is associated
with the log-gamma polymers. This log-gamma line ensemble enjoys a
random walk Gibbs resampling invariance that follows from the
integrable nature of the log-gamma gamma polymer model via the
geometric RSK correspondence. By exploiting such resampling
invariance, we show the tightness of this log-gamma line ensemble
under the weak noise scaling. Furthermore, a Gibbs property, as
enjoyed by the KPZ line ensemble, holds for all subsequential limits.

Fri Dec 06

Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Dec 06

Math Biology Seminar

2:30pm - VinH 209
Math Biology Seminar

Fri Dec 06

1:30pm - Vincent Hall 1

Fri Dec 06

Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Fri Dec 06

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Whitney Moore, University of Minnesota, Twin Cities
Fri Dec 06

IMA Data Science Lab Seminar

1:25pm - Lind 305
Probabilistic Preference Learning with the Mallows Rank Model for Incomplete Data
Arnoldo Frigessi, Oslo University Hospital
Abstract:

Personalized recommendations are useful to assist users in their choices in web-based market places, entertainment engines, information providers. Learning individual preferences is an important step. Users express their preferences by rating, ranking, (possibly inconsistently) comparing, liking and clicking items. Such data contain information about the individual users ranking of the items. Click-through data can be seen as (consistent) pair comparisons. The Mallows rank model allows to analyse rank data, but its computational complexity has limited its use to a particular form, based on Kendalls distance. We developed new computationally tractable methods for Bayesian inference in Mallows models that work with any right-invariant distance. Our method performs inference on the latent consensus ranking of all items and on the individual latent rankings by Bayesian augmentation. Current popular recommendation algorithms are based on matrix factorisations, have high accuracy and achieve good clickthrough rates. However diversity of the recommended items is often poor and most algorithms do not produce interpretable uncertainty quantifications of the recommendations. With a simulation study and real life data examples, we demonstrate that compared to matrix factorisation approaches, our Bayesian Mallows method makes personalized recommendations mpared to matrix factorisation approaches, our Bayesian Mallows method makes personalized recommendations.

Arnoldo Frigessi is professor of statistics at the University of Oslo, leads the Oslo Center for Biostatistics and Epidemiology and is director of BigInsight. BigInsight is a centre of excellence for research-based innovation, a consortium of industry, business, public actors and academia, developing model based machine learning methodologies for big data. Originally from Italy, where he had positions in Rome and Venice, he moved to Norway in 2019 as a researcher at the Norwegian Computing Centre, before he became professor at the University of Oslo.

Frigessi has developed statistical methodology motivated by specific problems in science, technology and industry. He has designed stochastic models to study principles, dynamics and patterns of complex dependence. Inference is usually based on computationally intensive stochastic algorithms. Currently, he has research collaborations in genomics, personalised therapy in cancer, infectious disease models, eHealth research, personalised and viral marketing, s

Thu Dec 05

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Dec 05

Colloquium

3:35pm - Vincent Hall 16
Modular forms on exceptional groups
Aaron Pollack, Duke
Abstract:

When G is a reductive (non-compact) Lie group, one can consider automorphic forms for G. These are functions on the locally symmetric space X_G associated to G that satisfy some sort of nice differential equation. When X_G has the structure of a complex manifold, the _modular forms_ for the group G are those automorphic forms that correspond to holomorphic functions on X_G. They possess close ties to arithmetic and algebraic geometry. For certain exceptional Lie groups G, the locally symmetric space X_G is not a complex manifold, yet nevertheless possesses a very special class of automorphic functions that behave similarly to the holomorphic modular forms above. Building upon work of Gan, Gross, Savin, and Wallach, I will define these modular forms and explain what is known about them.

Thu Dec 05

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
McCleary Philbin, University of Minnesota
Thu Dec 05

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Einstein's gravity and stability of black holes
Pei-Ken Hung, MIT
Abstract:

Though Einstein's fundamental theory of general relativity has already celebrated its one hundredth birthday, there are still many outstanding unsolved problems. The Kerr stability conjecture is one of the most important open problems, which posits that the Kerr metrics are stable solutions of the vacuum Einstein equation. Over the past decade, there have been huge advances towards this conjecture based on the study of wave equations in black hole spacetimes and structures in the Einstein equation. In this talk, I will discuss the recent progress in the stability problems with special focus on the wave gauge.

Wed Dec 04

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Dec 04

PDE Seminar

3:35pm - Vincent Hall 570
Multi-scale analysis of Jordan curves
Benjamin Jaye, Clemson University
Abstract:

In this talk we will describe how one can detect regularity in Jordan curves through analysis of associated geometric square functions. We will particularly focus on the resolution to a conjecture of L. Carleson. Joint work with Xavier Tolsa and Michele Villa (https://arxiv.org/abs/1909.08581).

Wed Dec 04

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Dec 03

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Dec 03

Colloquium

3:30pm - Vincent Hall 16
Mirror symmetry and canonical bases for quantum cluster algebras
Travis Mandel, Univ. of Edinburgh
Abstract:

Mirror symmetry is a phenomenon which relates the symplectic geometry of one space X to the algebraic geometry of another space Y. One consequence is that a canonical basis of regular functions on Y can be defined in terms of certain counts of holomorphic curves in X. I'll discuss the application of this to (quantum) cluster algebras --- certain combinatorially defined algebras whose definition was motivated by the appearance of canonical bases in representation theory and Teichmüller theory.

Tue Dec 03

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Dec 03

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Dec 03

IMA Data Science Lab Seminar

1:25pm - Lind 305
Exploiting Group and Geometric Structures for Massive Data Analysis
Zhizhen (Jane) Zhao, University of Illinois at Urbana-Champaign
Abstract:

In this talk, I will introduce a new unsupervised learning framework for data points that lie on or close to a smooth manifold naturally equipped with a group action. In many applications, such as cryo-electron microscopy image analysis and shape analysis, the dataset of interest consists of images or shapes of potentially high spatial resolution, and admits a natural group action that plays the role of a nuisance or latent variable that needs to be quotient out before useful information is revealed. We define the pairwise group-invariant distance and the corresponding optimal alignment. We construct a graph from the dataset, where each vertex represents a data point and the edges connect points with small group-invariant distance. In addition, each edge is associated with the estimated optimal alignment group. Inspired by the vector diffusion maps proposed by Singer and Wu, we explore the cycle consistency of the group transformations under multiple irreducible representations to define new similarity measures for the data. Utilizing the representation theoretic mechanism, multiple associated vector bundles can be constructed over the orbit space, providing multiple views for learning the geometry of the underlying base manifold from noisy observations. I will introduce three approaches to systematically combine the information from different representations, and show that by exploring the redundancy created artificially across irreducible representations of the transformation group, we can get drastically improved nearest neighbor identification, when a large portion of the true edges are corrupted. I will also show the application in cryo-electron microscopy image analysis.

Tue Dec 03

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
No Seminar
Mon Dec 02

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Towards personalized computer simulation of breast cancer treatment
&nbsp;Arnoldo&nbsp;Frigessi&nbsp;&nbsp;, &nbsp;University of Oslo&nbsp;&nbsp;
Abstract:

Current personalized cancer treatment is based on biomarkers which allow assigning each patient to a subtype of the disease, for which treatment has been established. Such stratifiedpatient treatments represent a first important step away from one-size-fits-all treatment.However, the accuracy of disease classification comes short in the granularity of thepersonalization: it assigns patients to one of a few classes, within which heterogeneity inresponse to therapy usually is still very large. In addition, the combinatorial explosivequantity of combinations of cancer drugs, doses and regimens, makes clinical testingimpossible. We propose a new strategy for personalised cancer therapy, based on producing acopy of the patients tumour in a computer, and to expose this synthetic copy to multiplepotential therapies. We show how mechanistic mathematical modelling, patient specificinference and simulation can be used to predict the effect of combination therapies in a breastcancer. The model accounts for complex interactions at the cellular and molecular level, andis able of bridging multiple spatial and temporal scales. The model is a combination ofordinary and partial differential equations, cellular automata and stochastic elements. Themodel is personalised by estimating multiple parameters from individual patient data,routinely acquired, including histopathology, imaging and molecular profiling. The resultsshow that mathematical models can be personalized to predict the effect of therapies in eachspecific patient. The approach is tested with data from five breast tumours collected in arecent neoadjuvant clinical phase II trial. The model predicted correctly the outcome after 12weeks treatment and showed by simulation how alternative treatment protocols would haveproduced different, and some times better, outcomes. This study is possibly the first onetowards personalized computer simulation of breast cancer treatment incorporating relevantbiologically-specific mechanisms and multi-type individual patient data in a mechanistic andmultiscale manner: a first step towards virtual treatment comparison.Xiaoran Lai, Oliver Geier, Thomas Fleischer, Øystein Garred, Elin Borgen, Simon Funke,Surendra Kumar, Marie Rognes, Therese Seierstad, Anne-Lise Børressen-Dale, VesselaKristensen, Olav Engebråten, Alvaro Köhn-Luque, and Arnoldo Frigessi, Tow

Mon Dec 02

Student Number Theory Seminar

3:35pm - Vincent Hall 1
Student Number Theory Seminar
Henry Twiss
Mon Dec 02

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Dec 02

Colloquium

3:35pm - Vincent Hall 570
Analysis and geometry of free boundaries: recent developments
Mariana Smit Vega Garcia, Western Washington University
Abstract:

In the applied sciences one is often confronted with free boundaries, which arise when the solution to a problem consists of a pair: a function u (often satisfying a partial differential equation (PDE)), and a set where this function has a specific behavior. Two central issues in the study of free boundary problems and related problems in calculus of variations and geometric measure theory are:(1) What is the optimal regularity of the solution u?
(2) How smooth is the free boundary (or how smooth is a certain set related to u)?

In this talk, I will overview recent developments in obstacle type problems and almost minimizers of Bernoulli-type functionals, illustrating techniques that can be used to tackle questions (1) and (2) in various settings.

The study of the classical obstacle problem - one of the most renowned free boundary problems - began in the 60s with the pioneering works of G. Stampacchia, H. Lewy and J. L. Lions. During the past five decades, it has led to beautiful and deep developments in the calculus of variations and geometric partial differential equations. Nowadays obstacle type problems continue to offer many challenges and their study is as active as ever.
While the classical obstacle problem arises from a minimization problem (as many other PDEs do), minimizing problems with noise lead to the notion of almost minimizers. Interestingly, though deeply connected to "standard" free boundary problems, almost minimizers do not satisfy a PDE as minimizers do, requiring additional tools from geometric measure theory to address (1) and (2).

Mon Dec 02

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 02

Topology Seminar

2:30pm - Ford Hall 110
Topology and Arithmetic Statistics
Weiyan Chen, University of Minnesota
Abstract:

Topology studies the shape of spaces. Arithmetic statistics studies the behavior of random algebraic objects such as integers and polynomials. I will talk about a circle of ideas connecting these two seemingly unrelated areas. To illuminate the connection, I will focus on three concrete examples: (1) the Burau representation of the braid groups, (2) analytic number theory for effective 0-cycles on a variety, and (3) cohomology of the space of multivariate irreducible polynomials. These projects are parts of a broader research program, with numerous contributions by topologists, algebraic geometers, and number theorists in the past decade, and lead to many future directions yet to be explored.
(PS. This will be a rehearsal of a job talk accessible to the general audience. Any comments or suggestions are appreciated.)

Mon Dec 02

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Nov 29

MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Nov 29

Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar
No Seminar
Fri Nov 29

Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Nov 29

Math Biology Seminar

2:30pm - VinH 209
Math Biology Seminar

Fri Nov 29

1:30pm - Vincent Hall 1

Fri Nov 29

Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Thu Nov 28

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Nov 28

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 28

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
TBA
Thu Nov 28

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Nov 27

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Nov 27

PDE Seminar

3:35pm - Vincent Hall 570
Quantitative Absolute Continuity of Harmonic Measure, and the Lp Dirichlet Problem
Steve Hofmann, University of Missouri
Abstract:

For a domain ? ? Rd, quantitative, scale-invariant absolute continuity (more precisely, the weak-A? property) of harmonic measure with respect to surface measure on ??, is equivalent to the solvability of the Dirichlet problem for Laplaces equation, with data in some Lp space on ??, with p < ?. Drawing an analogy to the famous Wiener criterion, which characterizes the domains in which the classical Dirichlet problem, with continuous boundary data, can be solved, it is of interest to find criteria for Lp solvability, thus allowing for singular boundary data. We shall review known results in this direction, in which (within the past 18 months) a rather complete picture has now emerged.

Wed Nov 27

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Nov 26

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Nov 26

Colloquium

3:35pm - Vincent Hall 16
Schrodinger solutions on sparse and spread-out sets
Xiumin Du, University of Maryland
Abstract:

If we want the solution to the Schrodinger equation to converge to its initial data pointwise, what's the minimal regularity condition for the initial data should be? I will present recent progress on this classic question of Carleson. This pointwise convergence problem is closely related to other problems in PDE and geometric measure theory, including spherical average Fourier decay rates of fractal measures, Falconer's distance set conjecture, etc. All these problems essentially ask how to control Schrodinger solutions on sparse and spread-out sets, which can be partially answered by several recent results derived from induction on scales and Bourgain-Demeter's decoupling theorem.

Tue Nov 26

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Nov 26

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Tue Nov 26

IMA Data Science Lab Seminar

1:25pm - Lind 305
Information Flow and Security Aspects in 1-2-1 Networks
Martina Cardone, University of Minnesota, Twin Cities
Abstract:

In this talk, we will discuss 1-2-1 networks, which offer a simple yet informative model for mmWave networks. In such networks, it is assumed that two nodes can communicate only if they point beams at each other, otherwise the signal is received well below the thermal noise floor. The focus of the talk will be on single unicast 1-2-1 networks, where the communication from a source to a destination is assisted by a number of relays. In the first part of the presentation, we will characterize the maximum flow of information over such 1-2-1 networks. In particular, we will show that the Shannon capacity can be approximated by routing information along a polynomial (in the network size) number of paths between the source and the destination, and that the scheduling of the node beam orientations can be efficiently performed. In the second part of the presentation, we will analyze the security aspect of such 1-2-1 networks in the presence of an external eavesdropper who wiretaps a set of edges of her choice. In particular, we will derive secure capacity results, which highlight fundamental differences between the traditional secure network coding and security over 1-2-1 networks.

Martina Cardone is currently a tenure-track Assistant Professor within the Electrical and Computer Engineering department at the University of Minnesota. She received her B.Sc. and her M.Sc. in Telecommunications Engineering from Politecnico di Torino, Italy in 2009 and 2011, respectively. As part of a double degree program, she also received a M.Sc. degrees in Telecommunications Engineering from Télécom ParisTech, France in 2011. In 2015, she received her Ph.D. in Electronics and Communications from Télécom ParisTech (with work done at Eurecom in Sophia Antipolis, France), where she worked with Professor Raymond Knopp and Professor Daniela Tuninetti. From July 2015 to August 2017 she was a post-doctoral research fellow in the Electrical and Computer Engineering department at the University of California, Los Angeles, where she worked with Professor Christina Fragouli. From November 2017 to January 2018, she was a post-doctoral associate in the Electrical and Computer Engineering department at the University of Minnesota. She regularly serves on the Technical Program Committee of IEEE workshops and conferences. Her main research interests are in network information theory, wireless communications, network privacy and secrecy, network coding and distributed computing. She was the reci

Tue Nov 26

Colloquium

1:25pm - Vincent Hall 570
K-stability and moduli spaces of Fano varieties
Yuchen Liu, Yale University
Abstract:

Fano varieties are positively curved algebraic varieties which form one of the three building blocks in the classification. Unlike the case of negatively curved varieties, moduli spaces of Fano varieties (even smooth ones) can fail to be Hausdorff. K-stability was originally invented as an algebro-geometric notion characterizing the existence of K\"ahler-Einstein metrics on Fano varieties. Recently, people have found strong evidence toward constructing compact Hausdorff moduli spaces of Fano varieties using K-stability. In this talk, I will discuss recent progress in this approach, including an algebraic proof of the existence of Fano K-moduli spaces, and describing these moduli spaces explicitly. This talk is partly based on joint works with H. Blum and C. Xu.

Tue Nov 26

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Nov 25

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Nov 25

Student Number Theory Seminar

3:35pm - Vincent Hall 1
Crystalline cohomology and Katz's conjecture
Shengkai Mao
Abstract:

Crystalline cohomology is a type of Weil cohomology theory that fills in the gap at $p$ in the family of $l$-adic cohomologies. It's introduced by Alexander Grothendieck and developed by Pierre Berthelot. We will briefly discuss what is crystalline cohomology and why we need it. With the help of Frobenius action, we can define a semi-linear morphism on crystalline cohomology which provides a Newton polygon. We will state the Katz's conjecture (which is proved by Mazur and Ogus) (slogan: Newton polygon lies above Hodge polygon) and show some applications (if time permits).

Mon Nov 25

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Nov 25

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Nov 25

Topology Seminar

2:30pm - Ford Hall 110
Topology Seminar
TBA
Mon Nov 25

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Mon Nov 25

Differential Geometry and Symplectic Topology Seminar

10:10am - Vincent Hall 203A
Differential Signatures and Algebraic Curves
Michael Ruddy,, Max Planck Institute
Abstract:

For the action of a group on the plane, the group equivalence problem for curves can be stated as: given two curves, decide if they are related by an element of the group. The signature method, using differential invariants, to answer the local group equivalence problem for smooth curves and its application to image science has been extensively studied. For planar algebraic curves under subgroups of the general linear group, we show that this provides a method to associate a unique algebraic curve to each equivalence class, the algebraic curve's signature curve. However, computing the implicit equation of the signature curve is a challenging problem. In this talk we consider signatures of algebraic curves, show how to compute the degree without computing its defining polynomial explicitly, and present some results on the structure of signature curves for generic algebraic curves of fixed degree. Additionally we show that this leads to a method to solve the group equivalence problem for algebraic curves using numerical algebraic geometry.

Fri Nov 22

MCFAM Seminar

5:30pm - Vincent Hall 16
The impact of negative interest rate policy and its effectiveness of stimulating economic growth
Perry Li, University of Minnesota

According to the Bloomberg Barclays Global Aggregate Index, there were $17 trillion (or 30%) bonds traded with negative yields within that popular fixed income benchmark, at the end of August 2019. Government bonds in Germany, Japan, and Switzerland all carry negative yields - meaning investors will lose money to hold them to maturity. How did we get here? Are those policies introduced by global central banks, after the 2008 financial crisis, effective (to spur inflation)? In this talk, I seek to use some case studies like reserve banking system, asset bubbles, and currency war to explore this topic.Bio: https://www.linkedin.com/in/liyuepeng/ Fri Nov 22 Combinatorics Seminar 3:30pm - Vincent Hall 570 A Pieri rule for key polynomials Danjoseph Quijada, USC Abstract: The Pieri rule for the product of a Schur function and a single row Schur function is notable for having an elegant bijective proof that can be intuited by the rules concise diagrammatic interpretation, to wit, by appending cells to a Young diagram. Now, key polynomials generalize Schur polynomials to a basis of the full polynomial ring, in which they also refine the Schubert basis via a nice formula. In this talk, I will describe a Pieri rule for the product of a key polynomial and a single row key polynomial that can be analogously interpreted as appending cells to a key diagram, albeit potentially dropping some cells in between each cell addition. I will also outline the main points of the rules bijective proof, and in the process hopefully illustrate the utility of understanding the rule from a diagrammatic perspective. Joint work with Sami Assaf. Fri Nov 22 Special Events and Seminars 3:30pm - Vincent Hall 20 Mass Scale Image Analysis For Automated Plant Phenotyping and Classification via Machine Learning Riley O'Neill, University of St. Thomas Abstract: The capacity to quantify crop architecture and morphology is foundational to the development of higher yielding cultivars via hybridization and genetic engineering. However, at the mass scale required by the science, manual plant phenotyping with physical instruments is arduous, time consuming, subjective, and a leading cause of undergraduate burnout in the UMN plant genetics department. While the process has been slightly improved with manual image analysis, such is almost as time consuming and remains subject to human error. Thereby, in efforts to further expedite phenotyping processes, circumvent human error, and provide more detailed analyses, we aim to completely automate plant phenotyping processes for the UMN plant genetics department and beyond. Working from over 15,000 soybean plants, weve advanced robust image processing platforms for measuring petiole and stem length, leaf area, leaf shape via signature curves, and branch angles via energy minimization in 2D, and begun preliminary work at 3D reconstructions from 2D data for 3D branch angles and further analyses. After data extraction and verification, we plan to implement clustering algorithms and machine learning to automatically group plant phenotypes as well as conduct principal component analysis to assemble an allometry space and identify the primary genes of influence. Fri Nov 22 AMAAZE 3:30pm - Vincent Hall 20 Mass Scale Image Analysis For Automated Plant Phenotyping and Classification via Machine Learning Riley O'Neill, University of St. Thomas Abstract: The capacity to quantify crop architecture and morphology is foundational to the development of higher yielding cultivars via hybridization and genetic engineering. However, at the mass scale required by the science, manual plant phenotyping with physical instruments is arduous, time consuming, subjective, and a leading cause of undergraduate burnout in the UMN plant genetics department. While the process has been slightly improved with manual image analysis, such is almost as time consuming and remains subject to human error. Thereby, in efforts to further expedite phenotyping processes, circumvent human error, and provide more detailed analyses, we aim to completely automate plant phenotyping processes for the UMN plant genetics department and beyond. Working from over 15,000 soybean plants, weve advanced robust image processing platforms for measuring petiole and stem length, leaf area, leaf shape via signature curves, and branch angles via energy minimization in 2D, and begun preliminary work at 3D reconstructions from 2D data for 3D branch angles and further analyses. After data extraction and verification, we plan to implement clustering algorithms and machine learning to automatically group plant phenotypes as well as conduct principal component analysis to assemble an allometry space and identify the primary genes of influence. Fri Nov 22 Probability Seminar 2:30pm - Vincent Hall 311 Spherical spin glass models Eliran Subag, New York University Abstract: How many critical points does a smooth random function on a high-dimensional space typically have at a given height? how are their distances distributed? what is the volume or geometry of the level sets? can we design efficient optimization algorithms for the random function? For the spherical spin glass models, those questions are closely related to the structure of the Gibbs measures, which have been extensively studied in physics since the 70s. I will start with an overview of the celebrated Parisi formula and ultrametricity property. I will then describe an alternative method to analyze the Gibbs measure using critical points, in the setting of the pure spherical models. Finally, I will explain how the latter can be extended to all spherical models, using another (soft) geometric approach, while at the same time making rigorous and generalizing the famous Thouless-Anderson-Palmer approach from physics. Fri Nov 22 Math Biology Seminar 2:30pm - VinH 209 Math Biology Seminar Fri Nov 22 Reading Seminar on Automorphic Forms 1:30pm - Vincent Hall 1 Reading Seminar on Automorphic Forms Fri Nov 22 Special Events and Seminars 1:25pm - Vincent Hall 213 "p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions TBA Fri Nov 22 IMA/MCIM Industrial Problems Seminar 1:25pm - Lind 305 Machine Learning Problems at Target Mauricio Flores, Target Corporation Abstract: PhD and Master's students would likely benefit the most from this talk. There will be some discussion on opportunities at Target. The introduction of this talk will provide an overview of the AI sciences organization at Target and discuss summer internship opportunities. The remainder of the talk will overview the kinds of machine learning problems Target deals with, and dive into three such problems, in the fields of recommender systems and computer vision. Mauricio Flores received his PhD in Applied Mathematics from the University of Minnesota in 2018, under the supervision of Jeff Calder & Gilad Lerman. He is currently a Lead AI Scientist at Target, where he builds machine learning as well as computer vision models for visually compatible recommendations, and more recently, for damage detection in Targets distribution centers. Thu Nov 21 Student Combinatorics Seminar 4:40pm - Vincent Hall 570 Student Combinatorics and Algebra seminar Thu Nov 21 Colloquium 3:35pm - Vincent Hall 16 Colloquium Thu Nov 21 Commutative Algebra Seminar 2:30pm - Vincent Hall 209 Commutative Algebra Seminar Erika Ordog, Duke University Thu Nov 21 Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Geometry of degenerating Calabi-Yau manifolds Ruobing Zhang, Stony Brook Abstract: This talk concerns a family of "collapsing" Ricci-flat Kähler manifolds, namely Calabi-Yau manifolds, converging to a lower dimensional limit, which develop singularities arising in various contexts such as metric Riemannian geometry, complex geometry and degenerating nonlinear equations. A primary aspect is to formulate how well behaved or badly behaved such spaces can be in terms of the recently developed regularity theory. Under the above framework, our next focus is on a longstanding fundamental problem which is to understand singularities of collapsing Ricci-flat metrics along an algebraically degenerating family. We will give accurate characterizations of such metrics and explain possible generalizations. Thu Nov 21 Topology Seminar 7:00am - Skybox LOWER (Legs + Butt) @ Skybox - Skybox Abstract: https://www.fitmetrix.io/webportal/schedulemobile/f9719b20-4914-e911-a97...(Legs%20%2B%20Butt)&dateRangeFrom=2019-11-21T07%3A00%3A00&dateRangeTo=2019-11-21T07%3A55%3A00&locationid=5854&classID=31918145 Wed Nov 20 Student Number Theory Seminar 3:35pm - Vincent Hall 6 Student Number Theory Seminar Wed Nov 20 PDE Seminar 3:35pm - Vincent Hall 570 Effective Poisson equation of density functional theory at positive temperature Li Chen, MIT Abstract: Density functional theory (DFT) has been a very successful effective theory of many-body quantum mechanics. In particular, the Kohn-Sham (KS) equations of DFT serve as an accurate model for the electron densities. The KS equations are a case of the Schrodinger-Poisson equations whose electron-electron effective interaction potential only depends on the density of electrons. When the number of electrons are limited, the KS equation can be solved quickly by numerical method at temperature T = 0. Since physically interesting settings are at T > 0, we study the KS equations at positive temperature and give an iterative scheme to construct solutions. One important class of electronic structures described by the KS equations is a crystalline lattice. At positive temperature, we show that a local perturbation to a crystalline structure induces an electric field governed by the Poisson equation. The latter equation emerges as an effective equation of the KS equations. This is a joint work with Israel M. Sigal. Wed Nov 20 Automorphic Forms and Number Theory 3:35pm - Vincent Hall 213 Automorphic Forms and Number Theory Tue Nov 19 Special Events and Seminars 4:30pm - Vincent Hall 301 Arithmetic Geometry Seminar Tue Nov 19 Colloquium 3:30pm - Vincent Hall 16 Colloquium Tue Nov 19 Dynamical Systems 2:30pm - Vincent Hall 209 Dynamical Systems Seminar Tue Nov 19 Colloquium 2:30pm - Vincent Hall 16 Random matrix theory and supersymmetry techniques Tatyana Shcherbyna, Princeton University Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a spacial structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY) . SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. Tue Nov 19 Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Tue Nov 19 IMA Data Science Lab Seminar 1:25pm - Lind 305 Robust Representation for Graph Data Dongmian Zou, University of Minnesota, Twin Cities Abstract: Modern data are usually high-dimensional with noise and corruption. A useful representation of data has to be robust and address the data structure. In this talk, I will first present a class of robust models called the scattering transform that can be used to generated features from graph data. In graph scattering transforms, the representation is generated in an unsupervised manner based on graph wavelets. It is approximately invariant to permutations and stable to signal or graph manipulations. Numerical results show that it works effectively for classification and community detection problems. Next, I will address how the structure of data can be found using autoencoders. Indeed, in the framework of autoencoders, graph scattering transform can be applied to the important task of graph generation. It shows state-of-the-art performance in link prediction and can be used to generate molecular samples. Tue Nov 19 Climate Seminar 11:15am - Vincent Hall 570 Climate Seminar TBA Tue Nov 19 Topology Seminar 10:30am - Skybox CORE @ Skybox - Skybox Mon Nov 18 Applied and Computational Math Colloquium 3:35pm - Vincent Hall 207 Applied and Computational Math Colloquium Mon Nov 18 Student Number Theory Seminar 3:35pm - Vincent Hall 1 The Casselman-Shalika Formula for GL_2 Emily Tibor Abstract: This talk will focus on the Casselman-Shalika formula for GL_2 over a non-Archimedean local field, which is an explicit formula for the values of the spherical Whittaker function. A good amount of time will be dedicated to explaining the necessary background including Whittaker models and spherical vectors, which come together to form the spherical Whittaker function. We will then be ready to discuss the formula, Casselman's method of calculating it, and its significance. Mon Nov 18 Applied and Computational Mathematics Seminar 3:35pm - Vincent Hall 6 Scalable Algorithms for Data-driven Inverse and Learning Problems Tan Bui-Thanh, UT-Austin Abstract: Inverse problems and uncertainty quantification (UQ) are pervasive in scientific discovery and decision-making for complex, natural, engineered, and societal systems. They are perhaps the most popular mathematical approaches for enabling predictive scientific simulations that integrate observational/experimental data, simulations and/or models. Unfortunately, inverse/UQ problems for practical complex systems possess these the simultaneous challenges: the large-scale forward problem challenge, the high dimensional parameter space challenge, and the big data challenge. To address the first challenge, we have developed parallel high-order (hybridized) discontinuous Galerkin methods to discretize complex forward PDEs. To address the second challenge, we have developed various approaches from model reduction to advanced Markov chain Monte Carlo methods to effectively explore high dimensional parameter spaces to compute posterior statistics. To address the last challenge, we have developed a randomized misfit approach that uncovers the interplay between the Johnson-Lindenstrauss and the Morozov's discrepancy principle to significantly reduce the dimension of the data without compromising the quality of the inverse solutions. In this talk we selectively present scalable and rigorous approaches to tackle these challenges for PDE-governed Bayesian inverse problems. Various numerical results for simple to complex PDEs will be presented to verify our algorithms and theoretical findings. If time permits, we will present our recent work on scientific machine learning for inverse and learning problems. Mon Nov 18 Topology Seminar 3:30pm - Vincent Hall 301 Topology Seminar: TBA Mon Nov 18 Topology Seminar 2:30pm - Ford Hall 110 Topology Seminar TBA Mon Nov 18 Cockburn's Seminar 2:30pm - Ford Hall B15 Cockburn's Seminar Fri Nov 15 MCFAM Seminar 5:30pm - Vincent Hall 16 Data Science in the Life Insurance Industry Gary Hatfield, Securian/University of Minnesota Abstract: Data Scientist has emerged as one of the hottest and most talked about jobs in the world today. In my talk, I will provide an overview of how data science has emerged in the insurance industry. I will give some examples of how data science is being applied in life insurance and describe how the Actuarial profession is adapting. Bio: https://mcfam.dl.umn.edu/people/gary-hatfield Fri Nov 15 Combinatorics Seminar 3:30pm - Vincent Hall 570 Simplicial generation of Chow rings of matroids Chris Eur, UC Berkeley Abstract: Matroids are combinatorial objects that capture the essence of linear independence. We first give a gentle introduction to the recent breakthrough in matroid theory, the Hodge theory of matroids, developed by Adiprasito, Huh, and Katz. By combining two prominent recent approaches to matroids, tropical geometric and Lie/Coxeter theoretic, we give a new presentation for the Chow ring of a matroid that further tightens the interaction between combinatorics and geometry of matroids. We discuss various applications, including a simplified proof of the main portion of the Hodge theory of matroids. This is joint work with Spencer Backman and Connor Simpson. Fri Nov 15 Probability Seminar 2:30pm - Vincent Hall 311 Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma Anna Kraut, Bonn Abstract: Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches. We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor. We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events. Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed. Fri Nov 15 Math Biology Seminar 2:30pm - Vincent Hall 311 Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma Anna Kraut, Bonn Abstract: Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches. We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor. We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events. Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed. Fri Nov 15 Dynamical Systems 2:30pm - Vincent Hall 20 The mathematics of taffy pulling Jean-Luc Thiffeault, University of Wisconsin Abstract: Taffy is a type of candy made by repeated 'pulling' (stretching andfolding) a mass of heated sugar. The purpose of pulling is to get air bubbles into the taffy, which gives it a nicer texture. Until the late 19th century, taffy was pulled by hand, an arduous task. The early 20th century saw an avalanche of new devices to mechanize the process. These devices have fascinating connections to the topological dynamics of surfaces, in particular with pseudo-Anosov maps. Special algebraic integers such as the Golden ratio and the lesser-known Silver ratio make an appearance, as well as more exotic numbers. We examine different designs from a mathematical perspective, and discuss their efficiency. This will be a "colloquium style" talk that should be accessible to graduate students. Fri Nov 15 Reading Seminar on Automorphic Forms 1:30pm - Vincent Hall 1 Reading Seminar on Automorphic Forms Fri Nov 15 Special Events and Seminars 1:25pm - Vincent Hall 213 "p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions TBA Fri Nov 15 IMA/MCIM Industrial Problems Seminar 1:25pm - Lind 305 Pipelines, Graphs, and the Language of Shopping: Architecting Next Gen Machine Learning Capabilities for Retail Jonah White, Best Buy Abstract: This talk will highlight the evolution of building out a data science capability in a retail environment as well as explore cutting-edge developments in constructing machine learning pipelines in the cloud, emerging advancements in time-series forecasting, applications of GPU accelerated graph processing for entity resolution, and how were adapting the latest research in language models to translate the language of shopping for the ultimate personalized experience Thu Nov 14 Student Combinatorics Seminar 4:40pm - Vincent Hall 570 Student Combinatorics and Algebra seminar Thu Nov 14 Colloquium 3:35pm - Vincent Hall 16$p$-adic estimates for exponential sums on curves Joe Kramer-Miller, UC Irvine Abstract: A central problem in number theory is that of finding rational or integer solutions to systems of polynomials in several variables. This leads one naturally to the slightly easier problems of finding solutions modulo a prime$p$. Using a discrete analogue of the Fourier transformation, this modulo$p$problem can be reformulated in terms of exponential sums. We will discuss$p$-adic properties of such exponential sums in the case of higher genus curves as well as connections to complex differential equations. Thu Nov 14 Commutative Algebra Seminar 2:30pm - Vincent Hall 209 Commutative Algebra Seminar Gennady Lyubeznik, University of Minnesota Thu Nov 14 Colloquium 2:30pm - Vincent Hall 16 Applications of Frobenius beyond prime characteristic. Daniel Hernández, Univ. of Kansas Abstract: Abstract: Recall that the Frobenius morphism is simply the map sending an element in a ring of prime characteristic$p>0$-- say, a polynomial with coefficients in a finite field -- to its$p$-th power. Though simple to define, Frobenius has proven to be a useful and effective tool in algebraic geometry, representation theory, number theory, and commutative algebra. Furthermore, and remarkably, some of the most interesting applications of Frobenius are to the study of objects defined over the complex numbers, and more generally, over a field of characteristic zero! In this talk, we will discuss some of these applications, with an eye towards classical singularity theory and birational algebraic geometry, both over the complex numbers. Thu Nov 14 Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Wed Nov 13 Student Number Theory Seminar 3:35pm - Vincent Hall 6 Student Number Theory Seminar Wed Nov 13 Automorphic Forms and Number Theory 3:35pm - Vincent Hall 213 Counting points and varieties and Malle's conjecture Andy Odesky, University of Michigan Wed Nov 13 PDE Seminar 3:30pm - Vincent Hall 570 Serrin Lecture - Localization for the Anderson-Bernoulli model on the integer lattice Charles Smart, University of Chicago Abstract: I will give a brief mathematical introduction to Anderson localization followed by a discussion of my recent work with Jian ding. In our work we establish localization near the edge for the Anderson Bernoulli model on the two dimensional lattice. Our proof follows the program of Bourgain--Kenig and uses a new unique continuation result inspired by Buhovsky--Logunov--Malinnikova--Sodin. I will also discuss recent work of by Li and Zhang on the three dimensional case. Tue Nov 12 Special Events and Seminars 4:30pm - Vincent Hall 301 Arithmetic Geometry Seminar Tue Nov 12 Colloquium 3:30pm - Vincent Hall 16 Colloquium Tue Nov 12 Dynamical Systems 2:30pm - Vincent Hall 209 Dynamical Systems Seminar Tue Nov 12 Colloquium 2:30pm - Vincent Hall 16 Unraveling Local Cohomology Emily Witt, Univ. of Kansas Abstract: Local cohomology modules are fundamental tools in commutative algebra, due to the algebraic and geometric information they carry. For instance, they can help determine the number of equations necessary to define an affine variety. Unfortunately, however, the application of local cohomology is limited by the fact that these modules are typically very large (e.g., not finitely generated), and can be difficult to determine explicitly. In this talk, we discuss new techniques developed to understand the structure of local cohomology (e.g., coming from invariant theory). We also describe recently-discovered "connectedness properties" of spectra that local cohomology encodes. Tue Nov 12 Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Tue Nov 12 IMA Data Science Lab Seminar 1:25pm - Lind 305 Latent Factor Models for Large-scale Data Xiaoou Li, University of Minnesota, Twin Cities Abstract: Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. Motivated by the applications of latent factor models to large-scale measurements which consist of many manifest variables (e.g. test items) and a large sample size, we study the properties of latent factor models under an asymptotic setting where both the number of manifest variables and the sample size grows to infinity. In this talk, I will introduce generalized latent factor models under exploratory and confirmatory settings. For the exploratory setting, we propose a constrained joint maximum likelihood approach for model estimation and investigate its theoretical properties. For the confirmatory setting, we study how the design information affects the identifiability and estimability of the model, and propose a rate-optimal estimator when the model is identifiable. The estimators can be efficiently computed through parallel computing. Our results provide insights on the design of large-scale measurement and have important implications on measurement validity. Tue Nov 12 Climate Seminar 11:15am - Vincent Hall 570 Climate Seminar TBA Mon Nov 11 Applied and Computational Math Colloquium 3:35pm - Vincent Hall 207 Applied and Computational Math Colloquium Mon Nov 11 Student Number Theory Seminar 3:35pm - Vincent Hall 1 Introduction to Rankin-Selberg Method Shengmei An Abstract: Rankin-Selberg method has been one of the most powerful techniques for studying the Langlands program. In this talk, we will start with the original simplest example of the Rankin-Selberg method, and then come to a more general case of the Rankin-Selberg method on GL_m*GL_n where we can reduce the global integral to the more accessible lovely local integrals so that we can establish some of the important analytic properties of the L-functions. Mon Nov 11 Applied and Computational Mathematics Seminar 3:35pm - Vincent Hall 6 Applied and Computational Mathematics Seminar Mon Nov 11 Topology Seminar 3:30pm - Vincent Hall 301 Topology Seminar: TBA Mon Nov 11 Topology Seminar 2:30pm - Ford Hall 110 Cochain models for the unit group of a differential graded algebra Tyler Lawson, University of Minnesota Abstract: Abstract not available. Mon Nov 11 Cockburn's Seminar 2:30pm - Ford Hall B15 Cockburn's Seminar Fri Nov 08 MCFAM Seminar 5:30pm - Vincent Hall 16 MCFAM Seminar Fri Nov 08 Combinatorics Seminar 3:30pm - Vincent Hall 570 Combinatorics via Deligne Categories Chris Ryba, MIT Abstract: The Deligne category Rep(S_t) can be thought of as "interpolating" the representation categories of symmetric groups. After describing this category, I will explain how a calculation in the Deligne category can be used to prove stability properties of permutation patterns within conjugacy classes (joint with Christian Gaetz). Fri Nov 08 Probability Seminar 2:30pm - Vincent Hall 311 "Robust Synchronization via Cycle Consistency Inference Yunpeng Shi, UMN Abstract: We propose a strategy for improving the existing methods for solving synchronization problems that arise from various computer vision tasks. Specifically, our strategy identifies severely corrupted relative measurements based on cycle consistency information. To the best of our knowledge, this paper provides the first exact recovery guarantees using cycle consistency information. This result holds for a noiseless but corrupted setting as long as the ratio of corrupted cycles per edge is sufficiently small. It further guarantees linear convergence to the desired solution. We also establish stability of the proposed algorithm to sub-Gaussian noise. Fri Nov 08 Math Biology Seminar 2:30pm - Vincent Hall 311 Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma Anna Kraut, Bonn Abstract: Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches. We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor. We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events. Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed. Fri Nov 08 Reading Seminar on Automorphic Forms 1:30pm - Vincent Hall 1 Reading Seminar on Automorphic Forms Fri Nov 08 Special Events and Seminars 1:25pm - Vincent Hall 213 "p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions Steven Sperber Thu Nov 07 Student Combinatorics Seminar 4:40pm - Vincent Hall 570 Student Combinatorics and Algebra seminar Thu Nov 07 Colloquium 3:35pm - Vincent Hall 16 Eisenstein Series on Loop Groups and their Metaplectic Covers Manish Patnaik, University of Alberta Abstract: Both the Langlands-Shahidi method of studying automorphic L-functions and approach via the theory of Weyl group multiple Dirichlet series to studying moments of L-functions now require new classes of groups with which to work. In this talk, I will explain our progress on extending these techniques to certain infinite-dimensional Kac-Moody groups, namely loop groups (and their metaplectic covers). Of note in our work is the presence of two quite different types of Eisenstein series that exist on the same group and which need to be considered in conjunction with one other. This is a report on joint work in progress with H. Garland, S.D. Miller, and A. Puskas. Thu Nov 07 Commutative Algebra Seminar 2:30pm - Vincent Hall 209 The spectral sequence of a filtered complex Gennady Lyubeznik, University of Minnesota Abstract: This is the third of a series of three talks on the spectral sequence of a filtered complex. This material is by now classical and is an important part of homological algebra. The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner. Thu Nov 07 Colloquium 2:30pm - Vincent Hall 16 On various questions (and answers) in High-dimensional probability Galyna Livshyts, Georgia Tech Abstract: In this talk, several topics from High-dimensional probability shall be discussed. This fascinating area is rich in beautiful problems, and several easy-to-state questions will be outlined. Further, some connections between them will be explained throughout the talk. I shall discuss several directions of my research. One direction is invertibility properties of inhomogeneous random matrices: I will present sharp estimates on the small ball behavior of the smallest singular value of a very general ensemble of random matrices, and will briefly explain the new tools I developed in order to obtain these estimates. Another direction is isoperimetric-type inequalities in high-dimensional probability. Such inequalities are intimately tied with concentration properties of probability measures. Among other results, I will present a refinement of the concavity properties of the standard gaussian measure in an n-dimensional euclidean space, under certain structural assumptions, such as symmetry. This result constitutes the best known to date estimate in the direction of the conjecture of Gardner and Zvavitch from 2007. The above topics will occupy most of the time of the presentation. In addition, I shall briefly mention other directions of my research, including noise-sensitivity estimates for convex sets, or, in other words, upper bounds on perimeters of convex sets with respect to various classes of probability distributions. If time permits, I will discuss my other results, such as small ball estimates for random vectors with independent coordinates, and partial progress towards Levi-Hadwiger illumination conjecture for convex sets in high dimensions. Thu Nov 07 Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Wed Nov 06 Student Number Theory Seminar 3:35pm - Vincent Hall 6 Student Number Theory Seminar Wed Nov 06 PDE Seminar 3:35pm - Vincent Hall 570 PDE Seminar Wed Nov 06 Automorphic Forms and Number Theory 3:35pm - Vincent Hall 213 The automorphic heat kernel from a geometric perspective Amy DeCelles, St. Thomas Tue Nov 05 Special Events and Seminars 4:30pm - Vincent Hall 301 Arithmetic Geometry Seminar Tue Nov 05 Colloquium 3:30pm - Vincent Hall 16 Colloquium Tue Nov 05 Dynamical Systems 2:30pm - Vincent Hall 209 Dynamical Systems Seminar Tue Nov 05 Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Tue Nov 05 IMA Data Science Lab Seminar 1:25pm - Lind 305 Topics in Sparse Recovery via Constrained Optimization: Least Sparsity, Solution Uniqueness, and Constrained Exact Recovery Seyedahmad Mousavi, University of Minnesota, Twin Cities Abstract: Sparse recovery finds numerous applications in different areas, for example, engineering, computer science, business, applied mathematics, and statistics. Sparse recovery is often formulated as relatively large-scale and challenging constrained (convex or nonconvex) optimization problems. Constraints are ubiquitous and important in many applications of sparse recovery, but they make analysis and computation nontrivial and require novel techniques to handle them. The goal of this talk is to present numerical and analytical techniques for constrained sparse recovery using convex analysis and optimization tools. Three topics are investigated in the realm of constrained sparse recovery. First, we analyze quantitative adverse properties of different$p$-norm-based optimization problems with$p>1$, such as generalized basis pursuit, basis pursuit denoising, ridge regression, and elastic net. We show that their optimal solutions are least sparse for almost all measurement matrices and measurement vectors. Second, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. We apply these solution uniqueness results to a broad class of$\ell_1$-minimization problems in constrained sparse optimization, such as basis pursuit, LASSO, and polyhedral gauge recovery. Third, we propose a constrained matching pursuit algorithm for constrained sparse recovery and develop uniform conditions for exact support and vector recovery on constraint sets. The exact recovery via this algorithm not only depends on a measurement matrix but also critically relies on a constraint set. Hence, we identify an important class of constraint sets, called coordinate projection admissible. We then use the conic hull structure of these sets together with constrained optimization techniques to establish sufficient conditions for uniform exact recovery via this algorithm on coordinate projection admissible sets. These conditions are expressed in terms of the restricted isometry-like and the restricted orthogonality-like constants Tue Nov 05 Climate Seminar 11:15am - Vincent Hall 570 Climate Seminar TBA Mon Nov 04 Applied and Computational Math Colloquium 3:35pm - Vincent Hall 207 Applied and Computational Math Colloquium Mon Nov 04 Student Number Theory Seminar 3:35pm - Vincent Hall 1 Rankin-Selberg Method May Shengmei Mon Nov 04 Applied and Computational Mathematics Seminar 3:35pm - Vincent Hall 6 Applied differential geometry and harmonic analysis in deep learning regularization Wei Zhu, Duke University Abstract: Deep neural networks (DNNs) have revolutionized machine learning by gradually replacing the traditional model-based algorithms with data-driven methods. While DNNs have proved very successful when large training sets are available, they typically have two shortcomings: First, when the training data are scarce, DNNs tend to suffer from overfitting. Second, the generalization ability of overparameterized DNNs still remains a mystery. In this talk, I will discuss two recent works to inject the modeling flavor back into deep learning to improve the generalization performance and interpretability of the DNN model. This is accomplished by DNN regularization through applied differential geometry and harmonic analysis. In the first part of the talk, I will explain how to improve the regularity of the DNN representation by enforcing a low-dimensionality constraint on the data-feature concatenation manifold. In the second part, I will discuss how to impose scale-equivariance in network representation by conducting joint convolutions across the space and the scaling group. The stability of the equivariant representation to nuisance input deformation is also proved under mild assumptions on the Fourier-Bessel norm of filter expansion coefficients. Mon Nov 04 Topology Seminar 3:30pm - Vincent Hall 301 Topology Seminar: TBA Mon Nov 04 Topology Seminar 2:30pm - Ford Hall 110 Topology Seminar TBA Mon Nov 04 Cockburn's Seminar 2:30pm - Ford Hall B15 Cockburn's Seminar Fri Nov 01 MCFAM Seminar 5:30pm - Vincent Hall 16 Extrapolative Expectations, Financial Frictions, and Asset Prices Yao Deng, University of Minnesota Abstract: I study how extrapolative expectations affect corporate real and financial activities and asset prices. Empirically, high misperception on earnings growth, a measure constructed to proxy for extrapolation, is associated with an increase in investment, debt issuance, equity issuance, and firm-level bond and stock prices in the short-term, but predicts a decline in all these activities and prices in the long-term. These patterns are more pronounced among small and financially constrained firms. Theoretically, I build a dynamic model with extrapolative expectations and financial frictions, and show that the interaction of these two frictions is crucial to explain the empirical findings. Intuitively, after a sequence of favorable shocks, agents extrapolate and become overoptimistic about future productivities. Firms invest and borrow more in the short-term. Lower perceived default probability improves financing conditions, further increasing investment and borrowing. Future realizations turn out worse than expected, making real and financial activities and asset prices subject to predictable reversals in the long-term.Bio: https://carlsonschool.umn.edu/faculty/yao-deng Fri Nov 01 Combinatorics Seminar 3:30pm - Vincent Hall 570 Combinatorics Seminar Dongkwan Kim, UMN Abstract: For a Coxeter group W, a W-graph is a graph which produces a nice basis of the corresponding representation of W and also describes the action of W on the basis elements. Even when W is finite and its irreducible characters are known, W-graphs are still useful for understanding representations of W. In this talk, I will talk about W-graphs when W is an (extended) affine symmetric group, especially when these graphs are associated with two-row partitions. Also I will discuss the connection between them and Lusztigs periodic W-graph. This work is joint with Pavlo Pylyavskyy. Fri Nov 01 Probability Seminar 2:30pm - Vincent Hall 311 Probability Seminar Fri Nov 01 Reading Seminar on Automorphic Forms 1:30pm - Vincent Hall 1 Reading Seminar on Automorphic Forms Fri Nov 01 Special Events and Seminars 1:25pm - Vincent Hall 213 p-Adic Banach Spaces and Completely Continuous Endomorphisms Steven Sperber Thu Oct 31 Student Combinatorics Seminar 4:40pm - Vincent Hall 570 Student Combinatorics and Algebra seminar Thu Oct 31 Colloquium 3:35pm - Vincent Hall 16 Differential operators on invariant rings Anurag Singh, University of Utah Abstract: Work of Levasseur and Stafford describes the rings of differential operators on various classical invariant rings of characteristic zero; in each of these cases, the differential operators form a simple ring. Towards an attack on the simplicity of rings of differential operators on invariant rings of reductive groups over the complex numbers, Smith and Van den Bergh asked if reduction modulo p works for differential operators in this context. In joint work with Jack Jeffries, we establish that this is not the case for various classical groups. Thu Oct 31 Commutative Algebra Seminar 2:30pm - Vincent Hall 209 Spectral sequences Gennady Lyubeznik, University of Minnesota Abstract: This is the first of a series of three talks on the spectral sequence of a filtered complex. This material is by now classical and is an important part of homological algebra. The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner. Thu Oct 31 Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Wed Oct 30 Student Number Theory Seminar 3:35pm - Vincent Hall 6 Student Number Theory Seminar Wed Oct 30 PDE Seminar 3:35pm - Vincent Hall 570 PDE Seminar Wed Oct 30 Automorphic Forms and Number Theory 3:35pm - Vincent Hall 213 Automorphic Forms and Number Theory Tue Oct 29 Special Events and Seminars 4:30pm - Vincent Hall 301 Arithmetic Geometry Seminar Tue Oct 29 Colloquium 3:30pm - Vincent Hall 16 Colloquium Tue Oct 29 Dynamical Systems 2:30pm - Vincent Hall 209 Dynamical Systems Seminar Tue Oct 29 Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Tue Oct 29 IMA Data Science Lab Seminar 1:25pm - Lind 305 Highly Likely Clusterable Data With No Cluster Mimi Boutin, Purdue University Abstract: Data generated as part of a real-life experiment is often quite organized. So much so that, in many cases, projecting the data onto a random line has a high probability of uncovering a clear division of the data into two well-separated groups. In other words, the data can be clustered with a high probability of success using a hyperplane whose normal vector direction is picked at random. We call such data highly likely clusterable. The clusters obtained in this fashion often do not seem compatible with a cluster structure in the original space. In fact, the data in the original space may not contain any cluster at all. This talk is about this surprising phenomenon. We will discuss empirical ways to detect it as well as how to exploit it to cluster datasets, especially datasets consisting of a small number of points in a high-dimensional space. We will also present a possible mathematical model that would explain this observed phenomenon. This is joint work with Alden Bradford (Purdue Math), Sangchun Han (Purdue ECE, now at Google) and Tarun Yellamraju (Purdue ECE, now at Qualcomm). Mireille (Mimi) Boutin graduated with a bachelors degree in Physics-Mathematics from the University of Montreal. She received the Ph.D. degree in Mathematics from the University of Minnesota under the direction of Peter J. Olver. She joined Purdue University after a post-doctorate with David Mumford, David Cooper, and Ben Kimia at Brown University, Rhode Island, followed by a post-doctorate with Stefan Muller at the Max Plank Institute for Mathematics in the Sciences in Leipzig, Germany. She is currently an Associate Professor in the School of Electrical and Computer Engineering, with a courtesy appointment in the Department of Mathematics. Her research is in the area of signal processing, machine learning, and applied mathematics. She is a three-time recipient of Purdues Seed for Success Award. She is also a recipient of the Eta Kappa Nu Outstanding Faculty Award, the Eta Kappa Nu Outstanding Teaching Award and the Wilfred Duke Hesselberth Award for Teaching Excellence. Tue Oct 29 Climate Seminar 11:15am - Vincent Hall 570 Convergence and Equilibrium for Stochastic Models of Ecological Disturbances James Broda, Bowdoin College Mon Oct 28 Applied and Computational Math Colloquium 3:35pm - Vincent Hall 207 Applied and Computational Math Colloquium Mon Oct 28 Student Number Theory Seminar 3:35pm - Vincent Hall 1 "Part 2: Representation Stability, Étale Cohomology and Combinatorics of Configuration Spaces over Finite Fields" David DeMark Abstract: After introducing the theory of FI-modules in 2012, the collaborative unit consisting of Thomas Church, Jordan Ellenberg and Benson Farb applied their framework to asymptotically stable counting problems in a certain classes of FI-varieties over finite fields in their 2013 paper Representation stability in cohomology and asymptotics for families of varieties over finite fields. The paper serves as a proof-of-concept, unifying a number of previously-known combinatorial results. The key to their method is the Grothendieck-Lefschetz fixed-point theorem with twisted statistics, which relates the rational cohomology of an algebraic variety over the complex numbers with the trace of the Frobenius map applied to the étale cohomology with coefficients in an$\ell$-adic sheaf of that variety over a finite field. In this talk, we shall introduce the Grothendieck-Lefschetz formula and its associated machinery as well as FI-modules and representation stability, then use these ideas to give an exposition of some results of Church, Ellenberg and Farb as they relate to configuration spaces and the braid group. Mon Oct 28 Applied and Computational Mathematics Seminar 3:35pm - Vincent Hall 6 Applied and Computational Mathematics Seminar Mon Oct 28 Topology Seminar 3:30pm - Vincent Hall 301 Topology Seminar: TBA Mon Oct 28 Topology Seminar 2:30pm - Ford Hall 110 Compactifying the étale topos Elden Elmanto, Harvard University Abstract: The speaker has long feared the technicalities and intricacies of equivariant stable homotopy theory. Fortunately, beginning with the work of Glasman, major simplification on the foundations of the subject has been made (cf. the work of Ayala-Mazel-Gee-Rozenblyum, Nikolaus-Scholze and the Barwick school). We offer another perspective (that the speaker has a chance of understanding) on equivariant stable homotopy theory, at least for the group C_2, via algebraic geometry. We view it as a way to remedy an infamous annoyance: the 2-étale cohomological dimension of the field of real numbers is infinite. We do this by identifying the genuine C_2-spectra with a category of motives based on Real algebraic geometry ala Scheiderer. This is joint work with Jay Shah. Mon Oct 28 Cockburn's Seminar 2:30pm - Ford Hall B15 Cockburn's Seminar Fri Oct 25 MCFAM Seminar 5:30pm - Vincent Hall 16 Mortgage Prepayment Behavior Messan Edorh and Bo Li, US Bank Abstract: According to the US Census Bureau, homeownership rates peaked during the first quarter of 2005 at 69.1% but fell to just 63.8% in the fourth quarter of 2015, a year when residential mortgage debt outstanding was still above ten trillion-dollar mark and mortgage origination was about$1.7T. Mortgage Back Security (MBS) originations have continued to experience a steady growth attracting investors, servicers, insurers, lenders, and GSEs (Government Sponsored Enterprises). In contrary, MBS market presented various financial risks including prepayment from the homeowners - be that voluntary or involuntary.

To manage the risks presented by the borrowers, modeling prepayment behavior is critical in the work banks do. Four fundamental components of mortgage prepayment activity will be examined in this presentation.

Fri Oct 25

Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorial Methods for Integrable Systems
Nick Ovenhouse.
Abstract:

An integrable Hamiltonian system is a dynamical system with "enough conserved quantities" to guarantee that it can, in principle, be solved, or "integrated". I will give some basic definitions of Poisson algebras and what it means to be integrable in this context. I will then show, by way of an example (namely the "pentagram map"), how some combinatorial techniques using weighted directed graphs can be used to model the system and demonstrate its integrability. This method also hints at connections with cluster algebras and Postnikov's constructions related to stratifications of the positive Grassmannian. Time permitting, I will also discuss recent work generalizing this example.

Fri Oct 25

Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar
Kevin Leder, UMN
Fri Oct 25

1:30pm - Vincent Hall 1

Fri Oct 25

Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Fri Oct 25

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Gamma Guidance - The Mathematics Applied to a Launch Vehicle
Gary Green, The Aerospace Corporation
Abstract:

The Boeing Inertial Upper Stage (IUS) launch vehicle was used to launch spacecraft from 1982 until 2004. The Gamma Guidance algorithm was used on board the IUS to select the ignition times, durations, and directions of engine firings. I will discuss the mathematics employed in Gamma Guidance as well as collateral on-board ;processes in order to illuminate how mathematics is applied in the launch setting.

Dr. Gary Green holds mathematics degrees from the Universities of Idaho, Michigan State, and Pennsylvania State. He taught mathematics at California State College Stanislaus before joining the Aerospace Corporation (www.aerospace.org), where he served as an applied mathematician and systems engineer in several capacities: employing numerical analysis to model launch vehicles, overseeing algorithm and software development for space systems, evaluating space system performance, and analyzing threats against space systems.

Thu Oct 24

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Oct 24

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 24

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Spectral Sequences
Abstract:

This is the first of a series of three talks on the spectral sequence of a filtered complex.
This material is by now classical and is an important part of homological algebra.
The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner.

Thu Oct 24

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Oct 23

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Oct 23

PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Oct 23

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Oct 22

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 22

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 22

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Oct 22

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 22

IMA Data Science Lab Seminar

1:25pm - Lind 305
Convergence Rates and Semiconvexity Estimates for the Continuum Limit of Nondominated Sorting
Brendan Cook, University of Minnesota, Twin Cities
Abstract:

Multiobjective optimization problems are ubiquitous in science and engineering contexts, and nondominated sorting is a sorting process fundamental to multiobjective optimization. Recently proposed approaches to nondominated sorting exploit an underlying PDE that arises in the continuum limit. The need for theoretical guarantees for nondominated sorting algorithms motivates the problem of finding rates of convergence for the continuum limit. In this talk I will introduce PDE techniques from the theory of viscosity solutions and show how they can be used to solve this problem. Furthermore, I will show how semiconvexity estimates can be used to bolster convergence rates, and discuss approaches to obtaining semiconvexity estimates. This talk is intended to be entirely self-contained, so no prior knowledge of PDE will be assumed.

Tue Oct 22

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Oct 21

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Oct 21

Student Number Theory Seminar

3:35pm - Vincent Hall 1
"Representation Stability, Étale Cohomology and Combinatorics of Configuration Spaces over Finite Fields"
David DeMark
Abstract:

After introducing the theory of FI-modules in 2012, the collaborative unit consisting of Thomas Church, Jordan Ellenberg and Benson Farb applied their framework to asymptotically stable counting problems in a certain classes of FI-varieties over finite fields in their 2013 paper Representation stability in cohomology and asymptotics for families of varieties over finite fields. The paper serves as a proof-of-concept, unifying a number of previously-known combinatorial results. The key to their method is the Grothendieck-Lefschetz fixed-point theorem with twisted statistics, which relates the rational cohomology of an algebraic variety over the complex numbers with the trace of the Frobenius map applied to the étale cohomology with coefficients in an $\ell$-adic sheaf of that variety over a finite field. In this talk, we shall introduce the Grothendieck-Lefschetz formula and its associated machinery as well as FI-modules and representation stability, then use these ideas to give an exposition of some results of Church, Ellenberg and Farb as they relate to configuration spaces and the braid group.

Mon Oct 21

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Oct 21

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 21

Topology Seminar

2:30pm - Ford Hall 110
Descent properties of topological Hochschild homology
Liam Keenan, University of Minnesota
Abstract:

Algebraic K-theory is an extremely rich but notoriously difficult invariant to compute. In order to make calculations tractible, topological Hochschild homology and topological cyclic homology were introduced, along with the Dennis and cyclotomic trace maps. A natural question to consider is whether or not these invariants are sheaves for various topologies arising in algebraic geometry. In fact, it turns out that topological Hochschild homology is a sheaf for the fpqc topology on connective commutative ring spectra. In this talk, I plan to introduce the language necessary and sketch the argument of this result.

Mon Oct 21

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Oct 18

MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Oct 18

Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar

Fri Oct 18

Probability Seminar

2:30pm - Vincent Hall 311
Rare events in the spectrum of random matrices
Kevin Leder, UMN
Abstract:

In this talk I will consider extreme behavior of the extremal eigenvalues of white Wishart matrices, which play an important role in multivariate analysis. I will focus on the case when the dimension of the feature p is much larger than or comparable to the number of observations n, a common situation in modern data analysis. I will discuss asymptotic approximations for the tail probabilities of the extremal eigenvalues. In addition, I will discuss the construction of an efficient Monte Carlo importance sampling algorithm to estimate the tail probabilities. Simulation results show that our method has the best performance among known approximation approaches, and furthermore provides an efficient and accurate way for evaluating the tail probabilities in practice. Based on joint work with Tiefieng Jiang and Gongjun Xu.

Fri Oct 18

1:30pm - Vincent Hall 1

Fri Oct 18

Special Events and Seminars

1:25pm - Vincent Hall 213
Trace Formula, continued
Steven Sperber, University of Minnesota
Thu Oct 17

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Oct 17

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 17

Colloquium

3:35pm - Vincent Hall 16
Hopf monoids relative to a hyperplane arrangement
Marcelo Aguiar, Cornell University
Abstract:

The talk is based on recent and ongoing work with Swapneel
Mahajan. We will introduce a notion of Hopf monoid relative to a real
hyperplane arrangement. When the latter is the braid arrangement, the
notion is closely related to that of a Hopf monoid in Joyal's category
of species, and to the classical notion of connected graded Hopf
algebra. We are able to extend many concepts and results from the
classical theory of connected Hopf algebras to this level. The
extended theory connects to the representation theory of a certain
finite dimensional algebra, the Tits algebra of the arrangement. This
perspective on Hopf theory is novel even when applied to the classical
case. We will outline our approach to generalizations of the classical
Leray-Samelson, Borel-Hopf, and Cartier-Milnor-Moore theorems to this
setting. Background on hyperplane arrangements will be reviewed.

Thu Oct 17

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Rebecca R.G., George Mason University
Thu Oct 17

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Oct 16

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Oct 16

PDE Seminar

3:35pm - Vincent Hall 570
Optimal local well-posedness for the derivative nonlinear Schrodinger's equation
Yu Deng, University of Southern California
Abstract:

In joint work with Andrea Nahmod and Haitian Yue, we prove local well-posedness for the derivative nonlinear Schrodinger's equation in Fourier-Lebesgue space which has the same scaling as H^s for any s>0. This closes the gap left open by the work of Grunrock-Herr where s>1/4. Here there is no trilinear estimate in any standard function space, instead we will construct the solution in a nonlinear submanifold (of a function space) by exploiting its structure. This is somehow inspired by the theory of para-controlled distributions that Gubinelli et al. developed for stochastic PDEs, but our arguments are purely deterministic.

Wed Oct 16

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Oct 15

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 15

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 15

Dynamical Systems

2:30pm - Vincent Hall 209
Forecasting U.S. elections with compartmental models of infection
Alexandria Volkening, Northwestern University
Abstract:

U.S. election forecasting involves polling likely voters, making assumptions about voter turnout, and accounting for various features such as state demographics and voting history. While political elections in the United States are decided at the state level, errors in forecasting are correlated between states. With the goal of shedding light on the forecasting process and exploring how states influence each other, we develop a framework for forecasting elections in the U.S. from the perspective of dynamical systems. Through a simple approach that borrows ideas from epidemiology, we show how to combine a compartmental model with public polling data from HuffPost and RealClearPolitics to forecast gubernatorial, senatorial, and presidential elections at the state level. Our results for the 2012 and 2016 U.S. races are largely in agreement with those of popular pollsters, and we use our new model to explore how subjective choices about uncertainty impact results. We conclude by comparing our forecasts for the senatorial and gubernatorial races in the U.S. midterm elections of 6 November 2018 with those of popular pollsters. This is joint work with Daniel Linder (Augusta Univ.), Mason Porter (UCLA), and Grzegorz Rempala (Ohio State Univ.)

Tue Oct 15

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 15

IMA Data Science Lab Seminar

12:30pm - Lind 305
Simple Approaches to Complicated Data Analysis
Deanna Needell, University of California, Los Angeles
Abstract:

Recent advances in technology have led to a monumental increase in large-scale data across many platforms. One mathematical model that has gained a lot of recent attention is the use of sparsity. Sparsity captures the idea that high dimensional signals often contain a very small amount of intrinsic information. Using this notion, one may design efficient low-dimensional representations of large-scale data as well as robust reconstruction methods for those representations. Binary, or one-bit, representations of data for example, arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this talk, we provide a brief background to sparsity and 1-bit measurements, and present new results on the problem of data classification with low computation and resource costs. We illustrate the utility of the proposed approach on recently acquired data about Lyme disease.

Tue Oct 15

Climate Seminar

11:15am - Vincent Hall 570
Climate and Non-Smooth Dynamics
Cameron Thieme, School of Mathematics
Mon Oct 14

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Oct 14

Student Number Theory Seminar

3:35pm - Vincent Hall 1
Arithmetic Speculation on a Combinatorial Lemma
Eric Stuckey
Abstract:

Reflection groups are an object in classical geometry with deep connections to Lie theory, representation theory, algebraic geometry, invariant theory, and combinatorics. The first half of the talk will give a quick introduction to various flavors of reflection groups. In the second half of the talk I will state a lemma about a restricted class of reflection groups, and discuss an idea for how incorporating cyclotomic fields may allow us to remove that restriction.

Mon Oct 14

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Oct 14

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 14

Topology Seminar

2:30pm - Ford Hall 110
Second order terms in arithmetic statistics
Craig Westerland, University of Minnesota
Abstract:

The machinery of the Weil conjectures often allows us to relate the singular cohomology of the complex points of a scheme to the cardinality of its set of points over a finite field. When we apply these methods to a moduli scheme, we obtain an enumeration of the objects the moduli parameterizes. It's rare that we can actually fully compute the cohomology of these moduli spaces, but homological stability results often give a first order approximation to the homology.

In this talk, we'll explain how to obtain second order homological computations for a class of Hurwitz moduli spaces of branched covers; these yield second order terms in enumerating the moduli over finite fields. We may interpret these as second order terms in a function field analogue of the function which counts number fields, ordered by discriminant. Our second order terms match those of Taniguchi-Thorne/Bhargava-Shankar-Tsimerman in the cubic case, and give new predictions in other Galois settings.

This is joint (and ongoing) work with Berglund, Michel, and Tran.

Mon Oct 14

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Oct 11

MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Oct 11

Combinatorics Seminar

3:30pm - Vincent Hall 570
Kazhdan-Lusztig Immanants for k-Positive Matrices
Sunita Chepuri
Abstract:

Immanants are matrix functionals that generalize the determinant. One notable family of immanants are the Kazhdan-Lusztig immanants. These immanants are indexed by permutations and are defined as sums involving Kazhdan-Lusztig polynomials. One notable property of Kazhdan-Lustzig immanants is that they are nonnegative on totally positive matrices. We give a condition on permutations that allows us to extend this theorem to the setting of k-positive matrices. We also conjecture a larger class of permutations for which our theorem holds true.

Fri Oct 11

Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Oct 11

1:30pm - Vincent Hall 1

Fri Oct 11

Special Events and Seminars

1:25pm - Vincent Hall 213
Trace Formula (continued)
Steven Sperber, University of Minnesota
Fri Oct 11

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Data Science in Healthcare
Yinglong Guo, UnitedHealth Group
Abstract:

UnitedHealth Group Research and Development (UHG R&D) is working on creating, validating, testing, and refining innovations in the healthcare industry. Our data science team provides technical solutions by applying various statistical and machine learning methods to a vast amount of data in order to answer research questions. In this talk, I will give a brief introduction to my day-to-day experience as a data scientist. I will also discuss the methodology involved in several analyses of treatment outcomes for prostate cancer.

Thu Oct 10

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Oct 10

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 10

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Mike Loper, University of Minnesota
Thu Oct 10

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Oct 09

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Oct 09

PDE Seminar

3:35pm - Vincent Hall 570
Diffusion in the Mean for a Periodic Schrödinger Equation Perturbed by a Fluctuating Potential
Shiwen Zhang, UMN
Abstract:

We consider the solution to a tight-binding, periodic Schrödinger equation with a random potential evolving stochastically in time. If the potential evolves according to a stationary Markov process we obtain a positive, finite diffusion constant for the evolution of the solution. More generally, we show that the square amplitude of the wave packet, after diffusive rescaling, converges to a solution of the heat equation. (Joint work with J. Schenker and Z. Tilocco at the Michigan State University).

Wed Oct 09

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Oct 08

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 08

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 08

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Oct 08

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 08

IMA Data Science Lab Seminar

1:25pm - Lind 305
LectureParallel Transport Convolutional Neural Networks on Manifolds
Rongjie Lai, Rensselaer Polytechnic Institute
Abstract:

Convolution has played a prominent role in various applications in science and engineering for many years. It is also the most important operation in convolutional neural networks (CNNs). There has been a recent growth of interests of research in generalizing CNNs on 3D objects, often represented as compact manifolds. However, existing approaches cannot preserve all the desirable properties of Euclidean convolutions, namely compactly supported filters, directionality, transferability across different manifolds. In this talk, I will discuss our recent work on a new way of defining convolution on manifolds via parallel transport. This geometric way of defining parallel transport convolution (PTC) provides a natural combination of modeling and learning on manifolds. PTC allows for the construction of compactly supported filters and is also robust to manifold deformations. I will demonstrate its applications to shape analysis using deep neural networks based on parallel transportation convolutional networks (PTC-net).

Dr. Rongjie Lai received his Ph.D. degree in applied mathematics from the University of California, Los Angeles, He is currently an assistant professor at the Rensselaer polytechnic Institute. Dr. Lais research interests are mainly in modern scientific computing including developing mathematical and computational tools for analyzing and processing signals, images as well as unorganized data using methods of variational partial differential equations, computational differential geometry and learning. In 2018, Dr. Lai was granted an NSF CAREER award for his research in geometry and learning for manifold-structured data in 3D and higher dimension.

Tue Oct 08

Climate Seminar

11:15am - Vincent Hall 570
Permafrost Response to Climate Change via Budykos Model
Richard McGehee, UMN
Mon Oct 07

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Nonuniqueness in Dynamical Systems
Richard McGehee, University of Minnesota
Abstract:

Discontinuous vector fields arise naturally in some applications. In this presentation, a simple classical model of ocean circulation is introduced as an example of how discontinuities give rise to nonunique solutions. Standard bifurcation techniques often fail when the vector field is not smooth, and certainly fail when the vector field is discontinuous. However, some topological techniques seem to carry over, and a crude birfurcation theory can be extended to a large class of discontinuous systems.

Mon Oct 07

Student Number Theory Seminar

3:35pm - Vincent Hall 1
A Tour of the p-adic Representation Theory of GL_2
Katy Weber
Abstract:

We summarize the classification of representations of GL_2 over a p-adic field, emphasizing the relationship between these representations and automorphic forms and L-functions. Time permitting, we will also discuss Whittaker models of these representations and the Casselman-Shalika formula. This talk is meant to be a sketch of these results and how they fit into the bigger picture, and should be accessible even if you are not very familiar with representation theory.

Mon Oct 07

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Oct 07

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 07

Topology Seminar

2:30pm - Ford Hall 110
Topology Seminar

Mon Oct 07

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Oct 04

MCFAM Seminar

5:30pm - Vincent Hall 16
RANDOM RULES AND THE ANCIENT HISTORY OF SIMULATION
Arkady Shemyakin, University of St. Thomas&nbsp;
Abstract:

Modern approaches to simulation, involving Monte Carlo methods and randomized procedures of decision-making, are usually dated back to the mid-20th century and the arrival of the computer era. Deeper history goes back to the 19th and even 18th centuries and involves such devices as Galtons board and Buffons needle. However, one can argue that long before the invention of computers, older devices such as dice and their predecessors have been effectively used for games and divination. The idea of this paper is to review the use of ancient randomizing devices to trace the history of simulation and random rules of decision-making. Special attention will be paid to some contemporary cultures, which have preserved some unique elements of their ancient history: native cultures of the Americas, the Celtic civilizations of Ireland and Scotland, and the indigenous peoples of Northern and Central Asia (Altai and Siberia).Bio: https://www.stthomas.edu/mathematics/faculty/arkady-shemyakin.html

Fri Oct 04

Probability Seminar

3:30pm - Vincent Hall 311
Invertibility of inhomogenuous heavy-tailed matrices
Galyna Livshyts, Georgia Tech
Abstract:

We will show the sharp estimate on the behavior of the smallest singular value of random matrices under very general assumptions. One of the key steps in the proof is a result about the efficient discretization of the unit sphere in an n-dimensional euclidean space. This result allows us to work with very general random matrices. The proof of the result will be outlined. Partially based on the joint work with Tikhomirov and Vershynin.

Fri Oct 04

Combinatorics Seminar

3:30pm - Vincent Hall 570
Higher cluster categories and QFT dualities
Gregg Musiker
Abstract:

We present a unified mathematical framework that elegantly describes minimally supersymmetric gauge theories in various dimensions, and their dualities. Though this approach utilizes higher Ginzburg algebras and higher cluster categories (also known as m-cluster categories), we show that the constructions can be given explicitly and combinatorially. We emphasize the connections to cluster algebras and two classes of examples: one class related to toric geometry and giving rise to brane bricks, which are 3-dimensional analogues of certain bipartite graphs on surfaces, and one class corresponding to higher partial triangulations of surfaces. This is based on joint work with Sebastian Franco of City College of New York. No prior knowledge of Quantum Field Theories or Cluster Algebras will be assumed.

Fri Oct 04

Probability Seminar

2:30pm - Vincent Hall 311
Reconstruction problems on amenable graphs
Ahmed El Alaoui, Stanford University
Abstract:

We consider the problem of reconstructing a hidden assignment of random variables (x_1,, x_n) sitting on the nodes of a graph, given noisy observations of pairs (x_u, x_v) for every edge (u,v) of the graph. Such problems have been extensively studied when the underlying graph is mean-field (e.g., the complete graph, Erdos-Renyi, random regular,), in which case the existence of a `possible-but-hard phase where reconstruction is possible but computationally difficult is ubiquitous.

In contrast, the picture is dramatically different when the graph is amenable. I will represent a generic result about the optimality of local algorithms for computing marginals under a somewhat strong model of side information. Next, I will focus on Z_2 synchronization (aka planted Ising model) on the Euclidean lattice with weaker side information, and discuss a renormalization-based procedure for reconstructing the assignment.

Joint work with Andrea Montanari.

Fri Oct 04

1:30pm - Vincent Hall 1

Fri Oct 04

Special Events and Seminars

1:25pm - Vincent Hall 213
"Trace Formula, I"
Steven Sperber, University of Minnesota
Thu Oct 03

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Oct 03

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 03

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Mahrud Sayrafi, University of Minnesota
Abstract:

Let Q be a regular local ring. An ideal I in Q is said to be licci if it is in the linkage class of a complete intersection. Christensen, Veliche and Weyman conjectured that a perfect ideal of grade 3 in Q is licci if and only if its free resolution corresponds to Dynkin diagrams.

After introducing the theory of linkage, I will talk about the conjecture, how Dynkin diagrams are involved, and their approach in showing one direction of the conjecture in arXiv:1712.04016.

Thu Oct 03

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Thu Oct 03

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Language and Interaction in Minecraft
Abstract:

I will discuss a research program aimed at building a Minecraft assistant, in order to facilitate the study of agents that can complete tasks specified by dialogue, and eventually, to learn from dialogue interactions. I will describe the tools and platform we have built allowing players to interact with the agents and to record those interactions, and the data we have collected. In addition, I will describe an initial agent from which we (and hopefully others) can iterate.

Wed Oct 02

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Oct 02

PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Oct 02

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Oct 01

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 01

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 01

Dynamical Systems

2:30pm - Vincent Hall 209
Relative equilibrium configurations of gravitationally interacting rigid bodies
Rick Moeckel, University of Minnesota
Abstract:

Consider a collection of n rigid, massive bodies interacting according to their mutual gravitational attraction. A relative equilibrium motion is one where the entire configuration rotates rigidly and uniformly about a fixed axis  all of the bodies are phase locked. Such a motion is possible only for special positions and orientations of the bodies. A minimal energy motion is one which has the minimum possible energy in its fixed angular momentum level. While every minimal energy motion is a relative equilibrium motion, the main result here is that a relative equilibrium motion of n >= 3 disjoint rigid bodies is never an energy minimizer. Since energy minimizers are the expected final states produced by tidal interactions, phase locking of 3 or more bodies will not occur.

Tue Oct 01

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 01

IMA Data Science Lab Seminar

1:25pm - Lind 305
Citizen Science and Machine Learning at Zooniverse
Darryl Wright, University of Minnesota, Twin Cities
Abstract:

As researchers gather ever-larger datasets there is an increasing demand for citizen science and reliance on machine learning. We will introduce Zooniverse, the world's largest citizen science platform, and show how citizen scientists are helping researchers extract meaningful information from their data. But the demand for citizen scientists and the volumes of data they are being asked to process is beginning to tax even the abilities of our 1.8 million volunteers. We will show how machine learning is being deployed to ease some of this burden and show how machine learning and citizen science can empower each other to process data more efficiently than either alone.

Tue Oct 01

Climate Seminar

11:15am - Vincent Hall 570
"An Introduction to Budyko's Energy Balance Model"
Richard McGehee
Mon Sep 30

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Sep 30

Student Number Theory Seminar

3:35pm - Vincent Hall 1
Leading up to Dirichlets class number formula
Dev Hegde
Abstract:

The talk will give a historical introduction to number theory leading up to Dirichlets class number formula which was one of the biggest achievements of analytic methods in number theory. No background is necessary to understand the talk.

Mon Sep 30

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Sep 30

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 30

Topology Seminar

2:30pm - Ford Hall 110
Mysterious Duality
Sasha Voronov, University of Minnesota
Abstract:

Mysterious Duality was discovered by Iqbal, Neitzke, and Vafa in 2001. They noticed that toroidal compactifications of M-theory lead to the same series of combinatorial objects as del Pezzo surfaces do, along with numerous mysterious coincidences: both toroidal compactifications and del Pezzo surfaces give rise to the exceptional series E_k; the U-duality group corresponds to the Weyl group W(E_k), arising also as a group of automorphisms of the del Pezzo surface; a collection of various M- and D-branes corresponds to a set of divisors; the brane tension is related to the area of the corresponding divisor, etc. The mystery is that it is not at all clear where this duality comes from. In the talk, I will present another series of mathematical objects: certain versions of multiple loop spaces of the sphere S^4, which are, on the one hand, directly connected to M-theory and its combinatorics, and, on the hand, possess the same combinatorics as the del Pezzo surfaces. This is a report on an ongoing work with Hisham Sati.

Mon Sep 30

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Sep 27

MCFAM Seminar

5:30pm - Vincent Hall 16
Positive Matrices and Derivative Models
Abstract:

Principal components analysis has become widely used in a variety of fields. In finance and, more specifically, in the theory of interest rate derivative modeling, its use has been pioneered by R. Litterman and J. Scheinkman. Their key finding was that a few components explain most of the variance of treasury zero-coupon rates and that the first three eigenvectors represent level, slope and curvature changes on the curve. This result has been, since then, observed in various markets.Over the years, there have been several attempts at modeling correlation matrices displaying the observed effects as well as trying to understand what properties of the those matrices are responsible for the effect. Using recent results of the theory of positive matrices we characterize these matrices and, as an application, we shed light on some of the critiques to this methodology.Bio: http://mcfam.math.umn.edu/people/carlos-tolmasky

Fri Sep 27

Combinatorics Seminar

3:30pm - Vincent Hall 570
A positivity phenomenon in Elser's Gaussian-cluster percolation model
Galen Dorpalen-Barry, University of Minnesota
Abstract:

Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideration of numerical graph invariants which we call \textit{Elser numbers} \text{els}_k(G), where G is a connected graph and k a nonnegative integer. Elser had proven that \text{els}_1(G)=0 for all G. By interpreting the Elser numbers as Euler characteristics of appropriate simplicial complexes called \emph{nucleus complexes}, we prove that for all graphs G, they are nonpositive when k=0 and nonnegative for k\geq2. The last result confirms a conjecture of Elser. At the end, we will present an open problem naturally arising from our proof of Elser's conjecture.

Fri Sep 27

Probability Seminar

2:30pm - Vincent Hall 311
Random matrices, operators and analytic functions
Abstract:

The finite circular beta-ensembles and their point process scaling limit can be represented as the spectra of certain random differential operators. These operators can be realized on a single probability space so that the point process scaling limit is a consequence of an operator level limit. The construction allows the derivation of the scaling limit of the normalized characteristic polynomials of the finite models to a random analytic function. I will review these representations and constructions, and present a couple of applications.

Joint with B. Virág (Toronto).

Fri Sep 27

1:30pm - Vincent Hall 1

Fri Sep 27

Special Events and Seminars

1:25pm - Vincent Hall 213
A p-adic analytic interpolation of a finite field character, II
Steven Sperber, University of Minnesota
Fri Sep 27

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Sampling from an Alternate Universe: Overview of Privacy-preserving Synthetic Data
Abstract:

Data accessibility is important--publicly available data-sets support vital social science research, social programs and data-informed governance. In recent years, an increasing amount of data has been curated and made generally available through sites like data.gov, IPUMS, and other resources, fueling the progress of research in Big Data. However, data with the most potential value for public good can also be the most privacy sensitive--such as data on abuse, STDS, extreme poverty, or mental health. These datasets exist, but may be redacted or entirely withheld from public view due to legal restrictions and the very real danger that anonymized individuals may be reidentified.

Privacy-preserving synthetic data provides a pathway to publicly release datasets that contain very sensitive information. The basic process consists of three parts: A generative model is built which captures the distribution of the original sensitive data, perturbation steps are applied to the model to improve its privacy properties (either formal or heuristic-based), and then the model is used to synthesize a new data set of synthetic individuals. The synthetic dataset preserves the significant properties of the original data, but because it contains no real people, it can be safely released to the public. When the distributional difference between the real and synthetic data mimics the difference between two subsamples of the original data, i.e. when privacy error mimics sampling error, we can think of the synthetic data as survey results from a parallel dimension: The same pattern of information as the original data, with no real people.

In this talk, I'll cover approaches to creating synthetic data, the difference between formal and heuristic-based privacy, and, importantly, quality metrics used to verify that the synthetic data is a good substitute for the original data (a challenging problem itself in a high dimensional feature space). High quality synthetic data is a rapidly progressing research area, with both promising success stories and an exciting frontier of open problems.

Thu Sep 26

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Sep 26

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Sep 26

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Global Sections of Toric Vector Bundles
Jorin Schug
Abstract:

This talk will continue to follow the "Parliament of Polytopes" paper by Di Rocco, Jabbusch, and Smith. I'll discuss the result that the T-equivariant generators for the global sections of a toric vector bundle E correspond to the lattice points in the parliament of polytopes for E and look to understand this result for some examples, including direct sums of line bundles.

Thu Sep 26

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Sep 25

PDE Seminar

3:35pm - Vincent Hall 570
Random Tug of War games for the p-Laplacian
Marta Lewicka, University of Pittsburgh
Abstract:

We propose a new dynamic programming principle related to the Dirichlet problem for the homogeneous p-Laplace equation in connection with the Tug of War games with noise. We also discuss similar approximations in presence of the Robin boundary conditions. For the proofs, we use martingale techniques involving various couplings of random walks and yielding estimates on the involved probabilistic representations.

Wed Sep 25

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Sep 25

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Sep 24

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Sep 24

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Sep 24

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Sep 24

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Sep 24

IMA Data Science Lab Seminar

1:25pm - Lind 305
The Geometry of Ambiguity in One-dimensional Phase Retrieval
Dan Edidin, University of Missouri
Abstract:

The phase retrieval problem is the problem of reconstructing an unknown signal from its Fourier intensity function. This problem has a long history in physics and engineering and occurs in contexts such as X-ray crystallography, speech processing and computational biology. As stated, the phase retrieval problem is ill-posed as there may be up to $2^N$ non-equivalent signals (called ambiguities) with the same Fourier intensity function. To enforce uniqueness additional constraints must be imposed.

In this talk we discuss the geometry of the space of ambiguities obtained by varying the signal. By understanding this geometry we prove a general result characterizing constraints that enforce a unique solution to the phase retrieval problem. This result was applied in work with Tamir Bendory and Yonina Eldar on blind phaseless short-time Fourier transform recovery.

Tue Sep 24

Climate Seminar

11:15am - Vincent Hall 570
An Introduction to Planetary Energy Balance
Richard McGehee, University of Minnesota
Mon Sep 23

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Sep 23

Student Number Theory Seminar

3:35pm - Vincent Hall 1
Elliptic Curves
Claire Frechette
Mon Sep 23

Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Sep 23

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 23

Topology Seminar

2:30pm - Ford Hall 110
Homology class of Deligne-Lusztig varieties
Dongkwan Kim, University of Minnesota
Abstract:

Since first defined by Deligne and Lusztig, a Deligne-Lusztig variety has become unavoidable when studying the representation theory of finite groups of Lie type. This is a certain subvariety of the flag variety of the corresponding reductive group, and its cohomology groups are naturally endowed with the action such finite groups, which in turn gives a decomposition of irreducible representations called Lusztig series. In this talk, I will briefly discuss the background of Deligne-Lusztig theory and provide a formula to calculate the homology class of Deligne-Lusztig varieties in the Chow group of the flag variety. If time permits, I will also discuss their analogues.

Mon Sep 23

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Sep 20

MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Student Research - Outcome analysis of Indexed Universal Life Insurance based on Monte Carlo Simulation
Songyu Yan and Ian Luo, University of Minnesota
Abstract:

Indexed Universal Life (IUL) Insurance was developed to harness thepower of equity market returns with downside protection. However IUL iscurrently illustrated using a static credited rate which masks market returnvolatility inherent in its structure. As a result, what policyholders see as expectedperformance maybe far from reality in many cases. In our research, we modeledthe pricing algorithms of major IUL products and applied scenario testing usingMonte Carlo simulation of indices used in IUL products. The statistical variance ofindices leads to vastly different results than what is currently demonstrated inmany cases, and this variance may cause the failure of the policy. Our researchindicates a better method for demonstrating policy performance would be basedon an outcome analysis rather than the static method currently in use.Bios: Songyu Yan: https://www.linkedin.com/in/songyu-yan-826bb2126/          Ian Luo: https://www.linkedin.com/in/yifei-luo-9051b1170/

Fri Sep 20

Combinatorics Seminar

3:30pm - Vincent Hall 570
Cyclic Sieving for planet partitions and symmetry
Sam Hopkins., University of Minnesota
Abstract:

The cyclic sieving phenomenon of Reiner, Stanton, and White says that we can often count fixed points for a cyclic group acting on a combinatorial set by plugging roots of unity into a polynomial related to this set. One of the most impressive instances of the cyclic sieving phenomenon is a theorem of Rhoades asserting that the set of plane partitions in a rectangular box under the action of promotion exhibits cyclic sieving. In Rhoades's result the sieving polynomial is the size generating function for these plane partitions, which has a well-known product formula due to MacMahon. We extend Rhoades's result by studying the interaction of promotion with symmetries of plane partitions. We obtain cyclic sieving-like formulas in this context where the relevant polynomial is the size generating function for symmetric plane partitions, whose product formula was conjectured by MacMahon and proved by Andrews. We then go on to consider the way the symmetries interact with rowmotion, another operator acting on plane partitions which is closely related to promotion. We end by explaining the connection of our work to some earlier conjectures we made concerning rowmotion acting on the P-partitions of various triangular posets P.

Fri Sep 20

Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Sep 20

1:30pm - Vincent Hall 1

Fri Sep 20

Special Events and Seminars

1:25pm - Vincent Hall 213
A p-adic analytic interpolation of a finite field character
Steven Sperber, University of Minnesota
Fri Sep 20

IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 409
SIAM Industrial Panel
-, -
Thu Sep 19

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Sep 19

Colloquium

3:35pm - Vincent Hall 16
The Langlands Program: An Introduction and Recent Progress
Solomon Friedberg,, Boston College
Abstract:

The Langlands Program, connecting algebra, analysis and geometry in diverse ways, is foundational to modern number theory. I will introduce this program and indicate some recent progress. As we shall see, a great deal still remains to be done.

Thu Sep 19

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Sep 19

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar

Thu Sep 19

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
D=4, N=1 Compactifications of Maximal Supergravities via Generalised Geometry - Kahler potentials, superpotentials and moduli
David Tennnyson, Imperial College London
Abstract:

We analyse compactifications of 11 dimensional or type II supergravity down to 4 dimensional Minkowski space for generic flux and generic internal Killing spinors. We note the failure of conventional differential geometry to capture the generic features of the theory and show that the correct formalism comes in the form of a closed form Leibniz algebroid - or as we call it in the physics community, generalised geometry. Our structure is similar to the generalised geometry of Hitchin, but now the structure group is the non-compact exceptional group E_{7(7)}x R^{+}. It turns out that having N=1 supersymmetry in the effective theory on Minkowski space is equivalent to an integrable SU(7) structure on the generalised tangent bundle. We provide the tensors that define the SU(7) structure and give the integrability conditions. Finally we provide an expression for the Kahler potential on the space of structures, the superpotential of the lower dimensional theory, and we explore the moduli of these structures giving explicit answers in certain cases.

Wed Sep 18

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Sep 18

PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Sep 18

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Siegel's extensions of Epstein zeta functions as Eisenstein series
Paul Garrett, University of Minnesota
Tue Sep 17

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Sep 17

Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Sep 17

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Sep 17

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Tue Sep 17

IMA Data Science Lab Seminar

1:25pm - Lind 305
Optimal Recovery under Approximability Models, with Applications
Simon Foucart, Texas A & M University
Abstract:

For functions acquired through point evaluations, is there an optimal way to estimate a quantity of interest or even to approximate the functions in full? We give an affirmative answer to this question under the novel assumption that the functions belong to a model set defined by approximation capabilities. In fact, we produce implementable linear algorithms that are optimal in the worst-case setting. We present applications of the abstract theory in atmospheric science and in system identification.

Dr. Simon Foucart earned a Masters of Engineering from the Ecole Centrale Paris and a Masters of Mathematics from the University of Cambridge in 2001. In 2006, he received his Ph.D. in Mathematics at the University of Cambridge, specializing in Approximation Theory. After two postdoctoral positions at Vanderbilt University and Université Paris 6, he joined Drexel University in 2010 before moving to the University of Georgia in 2013. Since 2015, he has been with Texas A&M University, where is now professor. His recent work focuses on the field of Compressive Sensing, whose theory is exposed in the book A Mathematical Introduction to Compressive Sensing he coauthored with Holger Rauhut. Dr. Foucarts research was recognized by the Journal of Complexity, from which he received the 2010 Best Paper Award. Dr. Foucarts current interests also include the mathematical aspects of Metagenomics, Optimization, Deep Learning and Data Science at Large

Tue Sep 17

Climate Seminar

11:15am - Vincent Hall 570
The Scientific Case for Anthropogenic Warming II
Richard McGehee, University of Minnesota
Mon Sep 16

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Sep 16

Student Number Theory Seminar

3:35pm - Vincent Hall 1
A Brief Introduction to L-Functions
Joe Dickinson
Abstract:

Like Andy's talk last week, this week will be another introductory talk; the topic is L-functions. We will start with a discussion of Dirichlet's use of L-series to show the infinitude of primes in arithmetic progressions, then proceed to how L-functions have become a major area of investigation. We will discuss only a sampling of topics, with the goal of motivating interest and setting the stage for future talks.

Mon Sep 16

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 16

Topology Seminar

2:30pm - Ford Hall 110
Transfer in the homology and cohomology of categories
Peter Webb, University of Minnesota
Abstract:

The cohomology of a category has many properties that extend those that are familiar when the category is a group. Second cohomology classifies equivalence classes of category extensions, first cohomology parametrizes conjugacy classes of splittings, first homology is the abelianization of the fundamental group, and second homology has a theory that extends that of the Schur multiplier. Defining restriction and corestriction maps on the homology of categories is problematic: most attempts to do this require induction and restriction functors to be adjoint on both sides, and this typically does not happen with categories. We describe an approach to defining these maps that includes all the situations where they can be defined in group cohomology, at least when the coefficient ring is a field. The approach uses bisets for categories, the construction by Bouc and Keller of a map on Hochschild homology associated to a bimodule, and the realization by Xu of category cohomology as a summand of Hochschild cohomology.

Mon Sep 16

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Sep 13

MCFAM Seminar

5:30pm - Vincent Hall 16
MFM Alumni/Student Panel: How the MFM Prepares You to Enter the Field of Quantitative Finance
MFM Alumni/Student Panel, Master of Financial Mathematics Program (MFM)
Abstract:

Learn from current students and MFM alumni in industry about the benefits of this professional master program. Panelists will talk about what attracted them to the program, how to make the most of your time in the MFM and why the practical, real-world learning helps you land jobs in quantitative risk analysis, hedging, trading, portfolio management, fintech, data analytics and other jobs that are hot in the field right now.

Fri Sep 13

Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar

Fri Sep 13

Probability Seminar

2:30pm - Vincent Hall 311
Critical behavior for percolation on graphs with given degrees
Souvik Dhara, MIT
Abstract:

We discuss critical behavior of percolation on finite random networks. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the Erdos-Renyi random graph (ERRG). Subsequently, there has been a surge in the literature, revealing several interesting scaling limits of these critical components, namely, the component size, diameter, or the component itself when viewed as a metric space. Fascinatingly, when the third moment of the asymptotic degree distribution is finite, many random graph models have been shown to exhibit a universality phenomenon in the sense that their scaling exponents and limit laws are the same as the ERRG. In contrast, when the asymptotic degree distribution is heavy-tailed (having an infinite third moment), the limit law turns out to be fundamentally different from the ERRG case and in particular, becomes sensitive to the precise asymptotics of the highest degree vertices.

In this talk, we will focus on random graphs with a prescribed degree sequence. We start by discussing recent scaling limit results, and explore the universality classes that arise from heavy-tailed networks. Of particular interest is a new universality class that arises when the asymptotic degree distribution has an infinite second moment. Not only it gives rise to a completely new universality class, it also exhibits several surprising features that have never been observed in any other universality class so far.

This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden and Sanchayan Sen.

Fri Sep 13

1:30pm - Vincent Hall 1

Fri Sep 13

Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Fri Sep 13

9:30am -
CANCELLED

Thu Sep 12

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Sep 12

Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Sep 12

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar

Thu Sep 12

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Wed Sep 11

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Sep 11

PDE Seminar

3:35pm - Vincent Hall 570
Parabolic problems with rough coefficients
Pierre Portal,, Australian National University
Abstract:

Using form methods, one can solve linear parabolic PDE in divergence form with $L^2$ data in appropriate energy spaces, even when the coefficients are merely bounded measurable in time and space, and no maximum principle is available. This goes back, at least, to the work of Lions and his school in the 1950s. When dealing with $L^p$ data, it is not so clear which $L^p$ like solution space one should use as a replacement of Lions energy space. Depending on the choice, one can solve, for instance, time dependent single equations (Aronson 1968), time independent systems for a range of values of $p$ (Auscher 2005), or stochastic problems with some spatial regularity (starting with Krylov 1994).
In this talk, I explain that, by choosing tent spaces as solution spaces (inspired by their role in elliptic boundary value problems on rough domains), one gets fairly general results, including both deterministic and stochastic problems, all values of $p$, systems as well as single equations, and rough coefficients in both time and space.

This summarises joint works with Pascal Auscher, Sylvie Monniaux, Jan van Neerven, and Mark Veraar.

Wed Sep 11

Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Sep 10

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Sep 10

3:30pm - VinH 16
Colloquium

Tue Sep 10

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Sep 10

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Tue Sep 10

IMA Data Science Lab Seminar

1:25pm - Lind 305
Taming Nonconvexity: From Smooth to Nonsmooth Problems and Beyond
Ju Sun, University of Minnesota, Twin Cities
Abstract:

Most applied problems we encounter can be naturally written as nonconvex optimization, for which
obtaining even a local minimizer is computationally hard in theory, never mind the global minimizer. In practice, however, simple numerical methods often work surprisingly well in finding high-quality solutions, e.g., training deep neural networks.

In this talk, I will describe our recent effort in bridging the mysterious theory-practice gap for nonconvex optimization, in the context of solving practical problems in signal processing, machine learning, and scientific imaging. 1) I will highlight a family of smooth nonconvex problems that can be solved to global optimality using simple numerical methods, independent of initialization. 2) The discovery, however, does not cover nonsmooth functions, which are frequently used to encode structural objects (e.g., sparsity) or achieve robustness. I will introduce tools from nonsmooth analysis, and demonstrate how nonsmooth, nonconvex problems can also be analyzed and solved in a provable manner. 3) Toward the end, I will provide examples to show how innovative problem formulation and physical design can help to tame nonconvexity.

Ju Sun is an assistant professor at the computer science & engineering department, University of Minnesota at Twin Cities. Prior to this, he was a postdoctoral scholar at Stanford University,
working with Professor Emmanuel Cand?s. He received his Ph.D. degree from Electrical Engineering of Columbia University in 2016 (2011--2016) and B.Eng. degree in Computer Engineering (with a minor in Mathematics) from the National University of Singapore in 2008 (2004--2008). His research interests span computer vision, machine learning, numerical optimization, signal/image processing, and high-dimensional data analysis. Recently, he is particularly fascinated by why simple numerical methods often solve nonconvex problems surprisingly well (on which he maintains a bibliographic webpage: http://sunju.org/research/nonconvex/ ) and the implication on representation learning. He won the best student paper award from SPARS'15 and honorable mention of doctoral thesis for the New World Mathematics Awards (NWMA) 2017.

Tue Sep 10

Climate Seminar

11:15am - Vincent Hall 570
"The Scientific Case for Anthropogenic Warming"
Richard McGehee, University of Minnesota
Mon Sep 09

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Emergent behavior in collective dynamics
Abstract:

Collective dynamics is driven by alignment that tend to self-organize the crowd and by different external forces that keep the crowd together. Different emerging equilibria are self-organized into clusters, flocks, tissues, parties, etc.

I will overview recent results on the hydrodynamics of large-time, large-crowd collective behavior, driven by different rules of engagement. In particular, I address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions.

Mon Sep 09

Student Number Theory Seminar

3:35pm - Vincent Hall 1
Student Number Theory Seminar

Mon Sep 09

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 09

Topology Seminar

2:30pm - Ford Hall 110
Cohomology of the space of complex irreducible polynomials in several variables
Weiyan Chen, University of Minnesota
Abstract:

We will show that the space of complex irreducible polynomials of degree d in n variables satisfies two forms of homological stability: first, its cohomology stabilizes as d increases, and second, its compactly supported cohomology stabilizes as n increases. Our topological results are inspired by counting results over finite fields due to Carlitz and Hyde.

Mon Sep 09

Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Sep 06

Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar

Fri Sep 06

Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Sep 06

1:30pm - Vincent Hall 1

Fri Sep 06

9:30am -
CANCELLED

Thu Sep 05

Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Sep 05

Colloquium

3:35pm - Vincent Hall 16
Colloquium - Canceled
Alina Chertock, NSCU
Abstract:

Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.

In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxisfluid system and will also be discussed.

Thu Sep 05

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar

Thu Sep 05

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Wed Sep 04

Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Sep 04

PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Tue Sep 03

Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Sep 03

3:30pm - VinH 16
Colloquium

Tue Sep 03

Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Sep 03

Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Tue Sep 03

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Sep 02

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Aug 30

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 30

9:30am -
CANCELLED

Thu Aug 29

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Tue Aug 27

Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Aug 26

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Aug 23

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 23

9:30am -
CANCELLED

Mon Aug 19

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Aug 16

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 16

9:30am -
CANCELLED

Wed Aug 14

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Aug 12

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 12

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Aug 09

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 09

9:30am -
CANCELLED

Wed Aug 07

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Aug 05

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 05

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Aug 02

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 02

9:30am -
CANCELLED

Wed Jul 31

Combinatorics Seminar

3:35pm - Vincent Hall 16
Hurwitz action of reflection factorizations of Coxeter elements
Sophiane Yahiatene, Bielefeld University
Abstract:

In the talk we will investigate a natural braid group action on factorizations of elements in reflection groups. In particular, we will consider reflection factorizations of Coxeter elements in Coxeter groups of finite rank and state conditions whether two factorizations lie in the same orbit under the natural action. The presented result extends the investigation of Lewis - Reiner (arXiv:1603.05969) to arbitrary Coxeter groups of finite rank. (j.w. Patrick Wegener)

Wed Jul 31

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jul 29

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 29

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jul 26

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jul 26

9:30am -
CANCELLED

Wed Jul 24

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Tue Jul 23

Combinatorics Seminar

3:35pm - Vincent Hall 113
Enumeration of bounded lecture hall tableaux
Jang Soo Kim,, Sungkyunkwan University
Abstract:

Recently Corteel and Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. In this talk, we enumerate bounded lecture hall tableaux. We show that their enumeration is closely related to standard and semistandard Young tableaux. We also show that the number of bounded lecture hall tableaux is the coefficient of the Schur expansion of s?(m+y1,...,m+yn). To prove this result, we use two main tools: non-intersecting lattice paths and bijections. In particular we use ideas developed by Krattenthaler to prove bijectively the hook content formula. This is joint work with Sylvie Corteel.

Mon Jul 22

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 22

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jul 19

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jul 19

9:30am -
CANCELLED

Thu Jul 18

Combinatorics Seminar

3:35pm - Vincent Hall 16
Fibers of maps to totally nonnegative spaces and the Fomin-Shapiro Conjecture
Patricia Hersh, North Carolina State University
Abstract:

Anders Björner and Joseph Bernstein raised the question of finding regular CW complexes naturally arising from representation theory having the intervals of Bruhat order as their posets of closure relations. Sergey Fomin and Michael Shapiro conjectured a solution, namely the link of the identity in the totally nonnegative real part of the unipotent radical of a Borel in a semisimple, simply connected algebraic group defined and split over the reals together with a family of related spaces indexed by the different Coxeter group elements. The Fomin-Shapiro conjecture indeed proved to be true, with the proof utilizing an interpretation of these stratified spaces as images of an intriguing family of maps - maps also arising in work of Lusztig related to canonical bases. I will start by reviewing some highlights of this story, then turn to recent joint work with Jim Davis and Ezra Miller regarding the structure of the fibers of these same maps.

Wed Jul 17

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jul 15

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 15

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jul 12

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jul 12

9:30am -
CANCELLED

Wed Jul 10

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jul 08

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 08

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jul 05

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jul 05

9:30am -
CANCELLED

Wed Jul 03

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jul 01

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 01

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jun 28

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jun 28

9:30am -
CANCELLED

Wed Jun 26

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jun 24

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 24

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jun 21

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jun 21

9:30am -
CANCELLED

Wed Jun 19

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jun 17

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 17

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jun 14

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jun 14

9:30am -
CANCELLED

Wed Jun 12

Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jun 10

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 10

Special Events and Seminars

1:30pm - Vincent Hall 364
Basic Operations on Representations
Andy Hardt
Abstract:

We continue our crash course in finite group representation theory by looking at some important operations on representations.

We start by defining the group algebra of a finite group; group representations naturally biject with modules over the group algebra.

After that, we'll talk through a variety of ways to construct new representations from old, such as restriction, induction, inflation, tensor product, and we may even squeeze in symmetric and exterior powers.

Fri Jun 07

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jun 07

9:30am -
CANCELLED

Thu Jun 06

Combinatorics Seminar

3:35pm - Vincent Hall 113
Chicken Nuggets and Numerical Semigroups
Abstract:

A numerical semigroup is a subset of N that is closed under addition, contains 0 and has finite complement in N. There are several fundamental invariants of a numerical semigroup S among which are the Frobenius number and genus of S, denoted F(S) and g(S), respectively. The quotient of a numerical semigroup S by a positive integer d is the set S/d={x|dx?S} which is also a numerical semigroup. In this talk, I will present some recent results showing the relation between the genus of S/d and the genus of S. If time permits, we will also talk about identities relating the Frobenius numbers and the genus of quotients of numerical semigroups that are generated by certain types of arithmetic progressions. This is joint work with S. Butler, C. Defant, Y. Gao, P.E. Harris, C. Hettle, Q. Liang, H. Nam, and A. Volk.

Wed Jun 05

Special Events and Seminars

2:00pm - Vincent Hall 570
AWM Talk
Mimi Boutin
Tue Jun 04

Special Events and Seminars

3:35pm - Vincent Hall 113
Special Events and Seminars

Tue Jun 04

Combinatorics Seminar

3:35pm - Vincent Hall 113
Counting core partitions and numerical semigroups using polytopes
Hayan Nam, University of California at Irvine
Abstract:

A partition is an aa-core partition if none of its hook lengths are divisible by aa. It is well known that the number of aa-core partitions is infinite and the number of simultaneous (a,b)(a,b)-core partitions is a generalized Catalan number if aa and bb are relatively prime. In the first half of the talk, we give an expression for the number of simultaneous (a1,a2,,ak)(a1,a2,,ak)-core partitions that is equal to the number of integer points in a polytope. In the second half, we discuss objects closely related to core partitions, called numerical semigroups, which are additive monoids that have finite complements in the set of non-negative integers. For a numerical semigroup SS, the genus of SS is the number of elements in ??SN?S and the multiplicity is the smallest nonzero element in SS. In 2008, Bras-Amorós conjectured that the number of numerical semigroups with genus gg is increasing as gg increases. Later, Kaplan posed a conjecture that implies Bras-Amorós conjecture. In this talk, we prove Kaplan's conjecture when the multiplicity is 4 or 6 by counting the number of integer points in a polytope. Moreover, we find a formula for the number of numerical semigroups with multiplicity 4 and genus gg.

Mon Jun 03

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri May 31

Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri May 31

9:30am -
CANCELLED

Wed May 29

Special Events and Seminars

1:30pm - Vincent Hall 206
Informal Fluids Seminar
Raj Beekie
Mon May 27

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri May 24

9:30am -
CANCELLED

Tue May 21

Math Physics Seminar

12:20pm - Vincent Hall 209
Second quantization of elliptic Calogero-Sutherland models
Bjorn Berntson
Abstract:

Calogero-Sutherland models are a class of completely integrable (quantum) many-body systems. In the most general case, particles interact pairwise through an elliptic potential. We discuss the second quantization of several elliptic Calogero-Sutherland models. In degenerate (trigonometric, rational) cases, there is a well-studied correspondence between Calogero-Sutherland systems and Benjamin-Ono equations, a nonlinear, integrable integro-differential equation. We discuss the correspondence in the elliptic regime, where second quantization of a particular system leads to a new two-component elliptic Benjamin-Ono equation. We construct a Lax pair for this equation via a Riemann-Hilbert problem on the torus. This is joint work with Edwin Langmann and Jonatan Lenells.

Mon May 20

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri May 17

9:30am -
CANCELLED

Thu May 16

Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu May 16

Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Tue May 14

Special Events and Seminars

3:30pm - Vincent Hall 570
Singularity formation for some solutions of the incompressible Euler equation
Tarek Elgindi
Abstract:

We describe a recent construction of self-similar blow-up solutions of the incompressible Euler equation. A consequence of the construction is that there exist finite-energy $C^{1,a}$ solutions to the Euler equation which develop a singularity in finite time for some range of $a>0$. The approach we follow is to isolate a simple non-linear equation which encodes the leading order dynamics of solutions to the Euler equation in some regimes and then prove that the simple equation has stable self-similar blow-up solutions.

Tue May 14

Math Physics Seminar

12:30pm - Vincent Hall 209
3rd order symmetries for systems on the 2-sphere and the 2 two-sheet 2-hyperboloid -- Superintegrability and cubic algebras
Willard Miller, University of Minnesota (Joint with Ian Marquette, University of Queensland, and Bjorn Berntson, KTH Royal Institute of Techn
Abstract:

There are many papers concerning 3rd and higher order superintegrable systems on 2D Euclidean space, particularly by Pavel Winternitz, his students and collaborators. However, we are not aware of similar studies on nonflat spaces. We decided to study the 2-sphere (with separation in polar coordinates) and the 2-hyperboloid (with separation in horospherical coordinates). The computations were very complex for these nonflat systems and the results less rich than for flat space, which is to be expected. In each case we have a Hamiltonian operator H a 2nd order symmetry operator A and compute a 3rd order symmetry operator B.
We classified the potentials which yielded

a nonzero B. They fall into 4 classes: 1) Systems that are 2nd order superintegrable, 2) Systems that are 3rd order superintegrable but do not generate a cubic algebra, 3) Systems with algebraically dependent generators A and B, 4) Systems that are 3rd order superintegrable with a cubic algebra.

We pay special attention to the class 3 cases which also occur for Euclidian space with little change. We call these functionally dependent superintegrable systems, and show that they always permit a computation of the A eigenfunctions by simple quadrature. For the hyperboloid we show that the TTW method applied to a 2nd order
superintegrable system in horospherical coordinates yields a 3rd order superintegrable system.

Tue May 14

Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Mon May 13

Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri May 10

First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri May 10