Past Seminars

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

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

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). 

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

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).

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. 

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.

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.

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.

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

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

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.

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.

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.

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.

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

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 

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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

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

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  

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.

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  

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.

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

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

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.

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     

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.

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  

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.

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

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).

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-

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)

Jacob Hegna (interned at Google)

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.

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.

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

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.

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.

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.

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.

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
researchers have access to a wide variety of mathematical infectious
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
realism for the epidemic in Connecticut. Using unique access to data
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.

Abstract:

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/).

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.

Abstract:

Testing django 2.2 upgrade

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  

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.

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.

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.

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.

Abstract:

Bio: https://www.linkedin.com/in/shaearmstrong/

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.

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.

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.

Abstract:

TBA

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.

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.

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.

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.