# Past Seminars

Mon Mar 18

7:30pm - Vincent Hall 213

Mon Mar 18

## Automorphic Forms and Number Theory

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

Mon Mar 18

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Mar 18

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Mar 18

## Topology Seminar

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

Fri Mar 15

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri Mar 15

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Cell Decompositions for Rank Two Quiver Grassmannians
Dylan Rupel, Michigan State University
##### Abstract:

A quiver Grassmannian is a variety parametrizing subrepresentations of a given quiver representation. Reineke has shown that all projective varieties can be realized as quiver Grassmannians. In this talk, I will study a class of smooth projective varieties arising as quiver Grassmannians for (truncated) preprojective representations of an n-Kronecker quiver, i.e. a quiver with two vertices and n parallel arrows between them. The main result I will present is a recursive construction of cell decompositions for these quiver Grassmannians motivated by the theory of rank two cluster algebras. If there is time I will discuss a combinatorial labeling of the cells by which their dimensions may conjecturally be directly computed. This is a report on joint work with Thorsten Weist.

Fri Mar 15

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Mar 15

## Probability Seminar

2:30pm - Vincent Hall 213
The generalized TAP free energy
Wei-Kuo Chen, UMN
##### Abstract:

Spin glasses are disordered spin systems initially invented by theoretical physicists with the aim of understanding some strange magnetic properties of certain alloys. In particular, over the past decades, the study of the Sherrington-Kirkpatrick (SK) mean-field model via the replica method has received great attention. In this talk, I will discuss another approach to studying the SK model proposed by Thouless-Anderson-Palmer (TAP). I will explain how the generalized TAP correction appears naturally and give the corresponding generalized TAP representation for the free energy. Based on a joint work with D. Panchenko and E. Subag.

Fri Mar 15

## Special Events and Seminars

2:30pm - Vincent Hall 1
Mathematical Physics, Algebraic Geometry, and Commutative Algebra
Fri Mar 15 1:25pm - Lind 305
Lecture
Karyn Sutton, The Institute for Disease Modeling
Fri Mar 15

9:30am -
CANCELLED

Thu Mar 14

## Colloquium

3:35pm - Vincent Hall 16
Short-Time Asymptotic Methods In Financial Mathematics
Jose Figueroa-Lopez, Washington University
##### Abstract:

In this talk, we will be concerned with the average values of certain random functionals of the path of a stochastic process during a given time period. High-order asymptotic characterizations of such values when the time period shrinks to 0 have a wide range of applications. In statistics, they are instrumental in establishing infill asymptotic properties of high-frequency based statistical methods of stochastic processes. In finance, they have been used as model selection and calibration tools based on near expiration option prices. In some Engineering problems, they also show up as a method to solve a problem in continuous time by looking at the analogous problem in discrete time and shrinking the time step to 0. These short-time asymptotic methods are especially useful in the study of complex models with jumps and stochastic volatility due to the lack of tractable formulas and efficient statistical and numerical procedures. In this talk, I will discuss some recent advances in the area and illustrate their broad relevance in several contexts.

Bio: Dr. Figueroa-López is a Professor in the Department of Mathematics and Statistics at Washington University in St. Louis. He currently serves as part of the executive committee and the chair of the statistics committee of the Department. Formerly he was Associate Professor of Statistics at Purdue University, where he served as Associate Director of the Computational Finance Program and as a member of the University Senate. Professor Figueroas ongoing research includes short-time asymptotics of jump-diffusion models, diffusion limits of Limit Order Book models, optimal limit order placement problems, market making via reinforced learning, and optimal tuning of high-frequency based econometric methods. He was awarded the NSF career award in 2012 and currently has two active NSF grants on the interplay of finance, statistics, and probability. He is an Associate Editor of the SIAM Journal on Financial Mathematics (SIFIN) and a former Associate Editor of Electronic Journal of Statistics.

Thu Mar 14

## Special Events and Seminars

1:25pm - Vincent Hall 113
Nearby cycles over general bases and duality
Weizhe Zheng, Chinese Academy of Sciences and Princeton University
##### Abstract:

Over one-dimensional bases, Gabber and Beilinson proved theorems on the commutation of the nearby cycle functor and the vanishing cycle functor with duality. In this talk, I will explain a way to unify the two theorems, confirming a prediction of Deligne. I will also discuss the case of higher-dimensional bases and applications to local acyclicity, following suggestions of Illusie and Gabber. This is joint work with Qing Lu.

Thu Mar 14

## Differential Geometry and Symplectic Topology Seminar

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

Thu Mar 14

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Towards Free Resolutions Over Scrolls
Aleksandra Sobieska-Snyder, Texas A&M
##### Abstract:

Free resolutions over the polynomial ring have a storied and active
record of study. However, resolutions over other rings are much more
mysterious; even simple examples can be infinite! In these cases, we
look to any combinatorics of the ring to glean information. This talk
will present a minimal free resolution of the ground field over the
semigroup ring arising from rational normal 2-scrolls, and (if time
permits) a computation of the Betti numbers of the ground field for all
rational normal k-scrolls.

Thu Mar 14

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Mar 14

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Mar 14

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Knots and Primes Part II: The Linking Number and Legendre Symbol
Katy Weber, University of Minnesota
##### Abstract:

We review the analogy between knots in 3-manifolds and prime ideals in number rings, and push it further to realize the Legendre symbol as the analogue of the (mod 2) linking number. This talk should be accessible even if you did knot attend seminar last week.

Thu Mar 14

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570

Wed Mar 13

7:30pm - Vincent Hall 213

Wed Mar 13

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Mar 13

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Postponed
Dongkwan Kim, University of Minnesota
##### Abstract:

This talk is postponed to March 27.

Tue Mar 12

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Mar 12

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Mar 12

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Tue Mar 12

## Special Events and Seminars

11:00am - Vincent 213
Compatible systems along the boundary
Weizhe Zheng, Chinese Academy of Sciences and Princeton University
##### Abstract:

A theorem of Deligne says that compatible systems of l-adic sheaves on a smooth curve over a finite field are compatible along the boundary. I will present an extension of Deligne's theorem to schemes of finite type over the ring of integers of a local field. This has applications to the equicharacteristic case of some conjectures on l-independence. I will also discuss the relationship with compatible wild ramification. This is joint work with Qing Lu.

Mon Mar 11

7:30pm - Vincent Hall 213

Mon Mar 11

## Automorphic Forms and Number Theory

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

Mon Mar 11

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Mar 11

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium
Canceled
Mon Mar 11

## Topology Seminar

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

Mon Mar 11

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Robust and Phaseless PCA (and Subspace Tracking)
Namrata Vaswani, Iowa State University
##### Abstract:

Principal Components Analysis (PCA), a.k.a. subspace learning, is one of the most widely used dimension reduction techniques that attempts to find a low-dimensional subspace approximation of a given dataset. PCA is a solved problem when the observed data is relatively clean and lies in (or close to) a low-dimensional subspace. However, in many modern applications, the data are often either incomplete (missing data) or corrupted by outliers. Robust PCA refers to this harder problem of PCA in the presence of entry-wise outliers (sparse corruptions). An important example application is video analytics when slow-changing videos are corrupted by foreground occlusions, e.g., by moving vehicles or persons. For long data sequences, e.g., long surveillance videos, if one tries to use a single subspace to represent the entire sequence, the required subspace dimension may be too large. For such data, a better model is to assume that the data subspace can change with time, albeit gradually. This problem of tracking data lying in a slowly changing subspace, while being robust to additive sparse outliers is referred to as Robust Subspace Tracking (RST). While robust PCA has received a lot of attention in the last decade, its dynamic version, RST, was largely open until recently. In a recent body of work, we have introduced the first provably correct and practically usable online solution framework for RST that we call Recursive Projected Compressive Sensing (ReProCS). Our most recent work from ICML 2018 shows that a simple ReProCS-based algorithm provides a provably fast and nearly (delay and memory) optimal RST solution under mild assumptions: weakened standard robust PCA assumptions and subspace change that is slow enough compared to the smallest magnitude outlier entry. Our theoretical claims are also backed by extensive experimental evidence for two video applications.

In new work, we have looked at what can be called the Phaseless PCA problem. This involves recovering a low-rank matrix from phaseless (magnitude-only) linear projections of each of its columns. It finds important applications in dynamic phaseless imaging applications, such as dynamic sub-diffraction imaging or Fourier ptychography, involving recovering a set of slowly-changing images that together form an approximately low-rank matrix (with each vectorized image being one column). We introduce a simple alternating minimization solution that can provable recover the low-rank matrix with sa

Fri Mar 08

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Mar 08

## MCFAM Seminar

5:30pm - Vincent Hall 16
Feb 2018 Volatility Event
Yuepeng Perry Li, CFA, FRM, Parametric Portfolio Associates LLC
##### Abstract:

On the Monday of February 5th 2018, VIX Index (measure of expected future volatility) spiked by 116% to 37.3, and massive turbulence was observed across global financial markets. During the talk, we will review this event and discuss on the following topics:

• How did we get there? --- Low volatility environment and the great snake of risk
• What happened? --- 2017s hottest trades went wrong, and several funds and firms (!) were effectively wiped out
• What did we learn?  Positioning, behavior, and never underestimate the risk of financial markets (convexity to volatility and VaR calcs)

Fri Mar 08

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Affine matrix-ball construction and its relation to representation theory
Dongkwan Kim, University of Minnesota
##### Abstract:

In 1985, Shi found a generalization of the Robinson-Schensted algorithm to (extended) affine symmetric groups and described their Kazhdan-Lusztig cells in terms of combinatorics. Recently, Chmutov, Lewis, Pylyavskyy, and Yudovina developed its generalization, called the affine matrix-ball construction (abbreviated AMBC). It provides a bijection from an (extended) affine symmetric group to the set of triples (P,Q,?) where P and Q are row-standard Young tableaux of the same shape and ? is an integer vector satisfying certain inequalities. In this talk, I will briefly explain this algorithm, and discuss how this is related to representation of (extended) affine symmetric groups, especially the asymptotic Hecke algebras introduced by Lusztig. This work is joint with Pavlo Pylyavskyy.

Fri Mar 08

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Mar 08

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Mar 08 1:25pm - Lind 305
Whitney Moore, University of Minnesota, Twin Cities
##### Abstract:

Internship/job searching is a multifaceted process that can summon many questions along the way! During this workshop, we will aim to address your most asked questions about getting started with your search, including:
- Where to find internships/jobs to apply for
- What to look for and how to read an internship/job posting
- What you can be doing now and over the summer to help prepare for your search.
There will be time to discuss more questions during the session, so come with your questions in hand!

Whitney Moore has been a Career Counselor in the CSE Career Center at the University of Minnesota since the fall of 2011. Her passion lies in living a life of positivity and inspiring others to do the same, particularly while navigating career and leadership development. In addition to her work at the U of M, Whitney is a past President of the Minnesota College and University Career Services Association (MCUCSA) and holds degrees from Gustavus Adolphus College and Minnesota State University, Mankato. Away from campus, Whitney is motivated by running with her dog, competing in triathlon, eating baked goods, and exploring MN with her husband. As an utter positivist, you can also find her musings on living with positivity on Instagram at @ThePositivistExplorer!

Fri Mar 08

8:30am -
CANCELLED

Thu Mar 07

## Differential Geometry and Symplectic Topology Seminar

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

Thu Mar 07

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Mar 07

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Mar 07

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Mar 07

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Mar 07

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Knots and Primes
Eric Stucky, University of Minnesota
##### Abstract:

In this talk we will outline the basic premise for the analogy between knots (in manifolds) and primes (in number fields). This analogy involves some rather heavy definitions; we will review the topological background as needed, while taking a more intuitive angle on the arithmetic machinery. Time permitting, we will briefly sketch an extension of the Frobenius automorphism which is a major tool in understanding the analogy between the Legendre symbol and the linking number.

Thu Mar 07

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570

Wed Mar 06

8:30pm - Vincent Hall 213

Wed Mar 06

## AMS Intro to Research Seminar

6:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Mar 06

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Generic Jordan forms and plane partitions
Sam Hopkins, University of Minnesota
##### Abstract:

We continue the introduction of the Garver-Patrias-Thomas paper by
exploring what the map from a quiver representations to its generic Jordan
form looks like in the case of a Type A quiver, and explain how this map is
related to bijections and generating functions for plane partitions.

Wed Mar 06

## PDE Seminar

3:35pm - Vincent Hall 570
Quantitative estimates of propagation of chaos for large systems of interacting particles
Zhenfu Wang, University of Pennsylvania
##### Abstract:

We present a new method to derive quantitative estimates proving the propagation of chaos for large stochastic or deterministic systems of interacting particles. Our approach requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit; and it can be applied to very singular kernels that are only in negative Sobolev spaces and include the Biot-Savart law for 2D Navier-Stokes and 2D Euler. Joint work with P.-E. Jabin.

Tue Mar 05

## Colloquium

3:35pm - Vincent Hall 16
Cohomology of Shimura varieties
Sug Woo Shin, U.C. Berkeley
##### Abstract:

Shimura varieties are a certain class of algebraic varieties over number fields with lots of symmetries, introduced by Shimura and Deligne nearly half a century ago. They have been playing a central role in number theory and other areas. Langlands proposed a program to compute the L-functions and cohomology of Shimura varieites in 1970s; this was refined by Langlands-Rapoport and Kottwitz in 1980s. I will review some old and recent results in this direction.

Tue Mar 05

## Dynamical Systems

2:30pm - Vincent Hall 313
Measuring attractor strength using bounded, nonautonomous control
Kate Meyer, UMN
##### Abstract:

A topological definition of an attractor leaves out metric information relevant to modeling real-world systems, particularly how far the attractor persists against perturbations and error. This talk will review some existing approaches to measuring the strength of an attractor in metric terms and will introduce the quantity intensity to generalize basin steepness to systems of autonomous ODEs in arbitrary dimension. One can compute an attractors intensity by probing a domain of attraction with bounded, non-autonomous control and tracking the sets reachable from the attractor. A connection between reachable sets and isolating blocks implies that an attractors intensity not only reflects its capacity to retain solutions under time-varying perturbations, but also gives a lower bound on the distance the attractor continues in the space of vector fields.
?

Tue Mar 05

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Mar 05

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Mar 04

8:30pm - Vincent Hall 213

Mon Mar 04

## Automorphic Forms and Number Theory

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

Mon Mar 04

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Mar 04

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Mar 04

## Topology Seminar

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

Mon Mar 04

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Peculiar Properties of Locally Linear Embedding -- Toward Theoretical Understanding of Unsupervised Learning
Hau-tieng Wu, Duke University
##### Abstract:

Since its introduction in 2000, the locally linear embedding (LLE) has been widely applied as an unsupervised learning tool. However, only few hand-waiving arguments are available to explain what is going on before 2018. For the sake of scientific soundness, we provide a systematic analysis of LLE, particularly under the manifold setup. In this talk, several theoretical results will be discussed. (1) We derive the corresponding kernel function, which in general is asymmetric and and not form a Markov process. (2) The regularization is critical. Different regularizations lead to dramatically different results. If chosen correctly, asymptotically we obtain the Laplace-Beltrami operator even under nonuniform sampling. (3) It has an intimate relationship with the local covariance analysis and tangent bundle structure. (4) When the boundary is not empty, we run into an interesting mixed-type differential equation. (5) An ingredient of the kernel provides a novel way to detect boundary, and hence a new approach to derive the Laplace-Beltrami operator with the Dirichlet boundary condition. If time permits, its relationship with several statistical topics like the locally linear regression and error in variable will be discussed. This is a joint work with Nan Wu.

Fri Mar 01

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Mar 01

## MCFAM Seminar

5:30pm - Vincent Hall 16
Introduction to model selection principles for data analysis in the era of Big Data
Jie Ding, School of Statistics - University of Minnesota
##### Abstract:

In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are employed, a crucial step is to select the most appropriate model or method from a set of candidates. Model selection is a key ingredient in data analysis for reliable and reproducible statistical inference or prediction, and thus central to scientific studies in fields such as ecology, economics, engineering, finance, political science, biology, and epidemiology. There has been a long history of model selection techniques that arise from researches in statistics, information theory, and signal processing. A considerable number of methods have been proposed, following different philosophies and exhibiting varying performances. The purpose of this talk is to bring an overview of them, in terms of their motivation, large sample performance, and applicability. I will provide practically relevant discussions on theoretical properties of state-of- the-art model selection approaches, and share some thoughts on controversial views on the practice of model selection.

Fri Mar 01

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Quotients of symmetric polynomial rings deforming the cohomology of the Grassmannian
Darij Grinberg
##### Abstract:

One of the many connections between Grassmannians and combinatorics is cohomological: The cohomology ring of a Grassmannian Gr(k,n) is a quotient of the ring S of symmetric polynomials in k variables. More precisely, it is the quotient of S by the ideal generated by the k consecutive complete homogeneous symmetric polynomials hn?k+1,hn?k+2,...,hn. We propose and begin to study a deformation of this quotient, in which the ideal is instead generated by hn?k+1?a1,hn?k+2?a2,...,hn?ak for some k fixed elements a1,a2,...,ak of the base ring. This generalizes both the classical and the quantum cohomology rings of Gr(k,n). We find two bases for the new quotient, as well as an S3-symmetry of its structure constants, a "rim hook rule" for straightening arbitrary Schur polynomials, and a fairly complicated Pieri rule. We conjecture that the structure constants are nonnegative in an appropriate sense (treating the ai as signed indeterminate), which suggests a geometric or combinatorial meaning for the quotient. There are multiple open questions and opportunities for further research.

Fri Mar 01

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Mar 01

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Mar 01 1:25pm - Lind 305
Lecture
Sohan Das, EVS, Inc.
Fri Mar 01

8:30am -
CANCELLED

Thu Feb 28

## Differential Geometry and Symplectic Topology Seminar

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

Thu Feb 28

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Feb 28

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Virtual Resolutions of Monomial Ideals
Jay Yang, University of Minnesota
##### Abstract:

Virtual resolutions as defined by Berkesch, Erman, and Smith,
provide a more geometrically meaningful generalization of free
resolutions in the case of subvarieties of a toric variety. In this
setting I prove an analog of Hilbert's syzygy theorem for virtual
resolutions of monomial ideals in toric varieties subject to some mild
conditions.

Thu Feb 28

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Feb 28

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Feb 28

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Finite Hecke Algebras and Their Characters
Andy Hardt, University of Minnesota
##### Abstract:

We explore some of the major results in the study of finite Hecke algebras and their character tables. These algebras are useful in the study of representations of finite Chevalley groups, and also appear in the study of quantum groups and knot/link invariants. We'll run through some equivalent definitions of this versatile object, and then talk about a couple approaches to its character theory. In particular, Starkey's rule is a combinatorial formula for the character table of the type A finite Hecke algebra. We'll briefly sketch a proof of this result and talk about the possibility for extension to other types. Starkey's rule allows us to calculate the weights of Ocneanu traces, which are important invariants in knot theory relating to type A Hecke algebras, and a type B version of Starkey's rule would give us insights into the type B analogue to Ocneanu traces.

Thu Feb 28

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570

Wed Feb 27

8:30pm - Vincent Hall 213

Wed Feb 27

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Jordan form data of quiver representations
Sam Hopkins, University of Minnesota
##### Abstract:

We introduce the paper of Garver, Patrias and Thomas: Minuscule reverse plane partitions via quiver representations, starting with a review of aspects of quiver representations.

Wed Feb 27

## AMS Intro to Research Seminar

12:20pm - Vincent Hall 570
AMS Intro to Research Seminar
Tue Feb 26

## Dynamical Systems

2:30pm - Vincent Hall 313
Spectral Consequences of Hidden Symmetry in Network Dynamical Systems
Eddie Nijholt, UIUC
##### Abstract:

Network dynamical systems play an important role in many fields of science; whenever there are agents whose time evolution is linked through some interaction structure, we may view the system as a network and model it accordingly. However, despite their prevalence, network dynamical systems are in general not well understood. One can identify two reasons for this. First of all, many coordinate changes and other transformations from well-known dynamical systems techniques do not respect the underlying network structure. Second of all, despite this somewhat ethereal' character, systems with a network structure often display behavior that is highly anomalous for general dynamical systems. Examples of this include very unusual bifurcation scenarios and high spectral degeneracies. As a possible explanation of this, it can be shown that a large class of network ODEs admit hidden symmetry, which may be discovered through the so-called fundamental network construction. In most cases, this underlying symmetry does not come from a group though, but rather from a more general algebraic structure such as a monoid or category. I will show how the fundamental network allows one to adapt techniques from dynamical systems theory to a network setting, and how some of the more unusual properties of networks may be explained. In doing so, I will mostly focus on spectral properties of linear network maps.
?

Tue Feb 26

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Feb 26

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Feb 25

8:30pm - Vincent Hall 213

Mon Feb 25

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Integral representations and meromorphic continuations of Eisenstein series and L-functions
Paul Garrett, University of Minnesota
Mon Feb 25

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Primal dual methods for Wasserstein gradient flows
Li Wang, University of Minnesota
##### Abstract:

We develop a variational method for nonlinear equations with a gradient flow structure. Such equations arise in applications of a wide range, such as porous median flows, material science, animal swarms, and chemotaxis. Our method builds on the JKO framework, which evolves the equation as a gradient flow with respect to the Wasserstein metric. As a result, our method has built-in positivity preserving, entropy decreasing properties, and overcomes stability issue due to the strong nonlinearity and degeneracy. Furthermore, our method is massively parallelizable, and thus extremely efficient in high dimensions. Upon discretization of the PDE constraint, we also prove the ??convergence of the fully discrete optimization towards the continuum JKO scheme.

Mon Feb 25

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Feb 25

## Topology Seminar

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

Mon Feb 25

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Strong Coresets for k-Median and Subspace Approximation: Goodbye Dimension
David Woodruff, Carnegie Mellon University
##### Abstract:

We obtain the first strong coresets for the k-median and subspace approximation problems with sum of distances objective function, on n points in d dimensions, with a number of weighted points that is independent of both n and d; namely our coresets have size poly(k/eps). A strong coreset (1+eps)-approximates the cost function for all possible sets of centers simultaneously. We also give input sparsity time algorithms for computing these coresets, which are fixed parameter tractable in k/eps. We obtain the result by introducing a new dimensionality reduction technique for coresets that significantly generalizes earlier results for squared Euclidean distances to sums of p-th powers of Euclidean distances for constant p >= 1.

Joint work with Christian Sohler

Fri Feb 22

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Feb 22

## MCFAM Seminar

5:30pm - Vincent Hall 112
The Prospect of a Forgivable Premium Insurance Policy
Kyle Jore, University of Minnesota
##### Abstract:

Despite low premiums and high subsidies, farmers view crop insurance programs as a gamble. One explanation, in a revenue protection program, is that farmers exhibit loss aversion when premiums are just above coverage. Introducing a model for conditional loss aversion (CLA), in the context of cumulative prospect theory, it can be shown that the introduction of a forgivable premium can remove the producers loss aversion. This would result in producers being willing to spend more on an insurance program and thus, allow for a reduction in the implied subsidy.

Fri Feb 22

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Counting factorizations in complex reflection groups
Joel Lewis, George Washington University
##### Abstract:

In this talk, I'll discuss ongoing work with Alejandro Morales generalizing a 30-year old result of Jackson on permutation enumeration: we consider the enumeration of arbitrary factorizations of a Coxeter element in a well generated finite complex reflection group, keeping track of the fixed space dimension of the factors. As in the case of the symmetric group, the factorization counts are ugly, so the goal is to choose a basis for the generating function in which the answer is nice. In the case of the infinite families of monomial matrices, we accomplish this via combinatorial arguments; a notion of transitivity of a factorization appears for the "type D" group G(m, m, n). I'll also describe some puzzling partial results in the exceptional cases.

Fri Feb 22

## PDE Seminar

3:35pm - Vincent Hall 311
Special PDE Seminar - How to obtain parabolic theorems from their elliptic counterparts
Blair Davey, City College of New York
##### Abstract:

Experts have long realized the parallels between elliptic and parabolic theory of partial differential equations. It is well-known that elliptic theory may be considered a static, or steady-state, version of parabolic theory. And in particular, if a parabolic estimate holds, then by eliminating the time parameter, one immediately arrives at the underlying elliptic statement. Producing a parabolic statement from an elliptic statement is not as straightforward. In this talk, we demonstrate a method for producing parabolic theorems from their elliptic analogs. Specifically, we show that an $L^2$ Carleman estimate for the heat operator may be obtained by taking a high-dimensional limit of $L^2$ Carleman estimates for the Laplacian. Other applications of this technique will be discussed.

Fri Feb 22

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Feb 22

## Probability Seminar

2:30pm - Vincent Hall 213
Largest Entries of Sample Correlation Matrices from Equi-correlated Normal Populations
Tiefeng Jiang, UMN
##### Abstract:

We the limiting distribution of the largest off-diagonal entry of the sample correlation matrices of high-dimensional Gaussian populations with equi-correlation structure. Assume the entries of the population distribution have a common correlation coefficient r >0 and both the population dimension p and the sample size n tend to infinity with log p=o(n^{1/3}).
As 0< r<1, we prove that the largest off-diagonal entry of the sample correlation matrix converges to a Gaussian distribution, and the same is true for the sample covariance matrix as 0< r<1/2. This differs substantially from a well-known result for the independent case where r=0, in which the above limiting distribution is an extreme-value distribution. We then study the phase transition between these two limiting distributions and identify the regime of r where the transition occurs. It turns out that the thresholds of such a regime depend on n and converge to zero. If r is less than the threshold, larger than the threshold or is equal to the threshold, the corresponding limiting distribution is the extreme-value distribution, the Gaussian distribution and a convolution of the two distributions, respectively. The proofs rely on a subtle use of the Chen-Stein Poisson approximation method, conditioning, a coupling to create independence and a special property of sample correlation matrices. The results are then applied to evaluating the power of a high-dimensional testing problem of identity correlation matrix.

Fri Feb 22 1:25pm - Lind 305
Industrial Problems in Digital Retail
Samantha Schumacher, Target Corporation
##### Abstract:

Target is rapidly growing into the online retail space. Behind that growth, there are a lot of advanced mathematical problems to solve. Some mathematics problems in supply chain are easy to spot (traveling salesman problem!), and some are less obvious. Well talk through at least 2 less-obvious problems which are currently being investigated by Targets Supply Chain analytics teams. The goal of this talk is to give insight into the broad range of problems we are solving at Target. Additionally, Ill spend a little time talking about solutions. What makes a good solution in Industry? What makes a good problem?

Samantha Schumacher has been working math problems at Target for the last 5 years. She currently leads an analytics and engineering team for the network planning & digital fulfillment of Targets supply chain. She has her PhD in applied mathematics from University of Minnesota and an undergraduate degree in theater from Smith College. So, if all goes according to plan, she will use those theater skills to keep the talk engaging! She is also the long-time author of the blog: www.SocialMathematics.net which considers the interaction of mathematics and the modern world.

Fri Feb 22

8:30am -
CANCELLED

Thu Feb 21

## Differential Geometry and Symplectic Topology Seminar

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

Thu Feb 21

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Feb 21

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Feb 21

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Feb 21

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Feb 21

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar - Cancelled

Thu Feb 21

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570

Wed Feb 20

8:30pm - Vincent Hall 213
TBD
Wed Feb 20

## AMS Intro to Research Seminar

6:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Feb 20

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Semisimplicity of Deligne's category Rep(S_t)
Peter Webb, University of Minnesota
##### Abstract:

Continuing to follow the paper of Comes and Ostrik, On blocks of Deligne's category Rep(S_t), we prove the result in Section 3 that the category is semisimple except for countably. many values of t. The proof is an interesting use of the characterization of semisimple algebras by non-degeneracy of the trace form.

Tue Feb 19

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Feb 19

## Math Physics Seminar

12:20pm - Vincent Hall 209
Invariants of Finite and Discrete Group Actions Via Moving Frames
Peter Olver
##### Abstract:

The equivariant moving frame method is adapted to algorithmically construct complete, minimal sets of generating invariants for finite or, more generally, discrete group actions, both linear and nonlinear. The resulting invariants are piecewise analytic and admit a rewrite rule that allows one to immediately express any other invariant (polynomial, rational, smooth, analytic, etc.) as a function of the generating invariants. The talk will be elementary and no a priori knowledge of invariant theory or moving frames will be assumed.

Tue Feb 19

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Feb 18

8:30pm - Vincent Hall 213

Mon Feb 18

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Integral Representations
Paul Garrett, University of Minnesota
Mon Feb 18

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Nonperturbative nonlinear effects in the dispersion relations for TE and TM plasmons on two-dimensional materials
Vera Andreeva
##### Abstract:

We analytically obtain the dispersion relations for transverse-electric (TE) and transverse-magnetic (TM) surface plasmon-polaritons in a nonlinear two-dimensional (2D) conducting material with inversion symmetry lying between two Kerr-type dielectric media. To this end, we use Maxwell's equations within the quasielectrostatic, weakly dissipative regime. We show that the wavelength and propagation distance of surface plasmons decrease due to the nonlinearity of the surrounding dielectric. In contrast, the effect of the nonlinearity of the 2D material depends on the signs of the real and imaginary parts of the third-order conductivity. Notably, the dispersion relations obtained by naively replacing the permittivity of the dielectric medium by its nonlinear counterpart in the respective dispersion relations of the linear regime are not accurate. We apply our analysis to the case of doped graphene and make predictions for the surface plasmon wavelength and propagation distance.

Mon Feb 18

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Feb 18

## Topology Seminar

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

Fri Feb 15

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Feb 15

## MCFAM Seminar

5:30pm - Vincent Hall 16
Simulating the Greeks of American Options
P.A. (Phuong Anh) Nguyen, University of Minnesota
##### Abstract:

Abstract: In this paper, we implement an efficient simulation-based method for estimating the Greeks of American options. We perform a least square regression to determine the optimal stopping rule that is applied to calculate the Greeks, which are derived via a path-wise derivative approach. We prove that this method provides asymptotically unbiased simulation estimators for the Greeks. In addition, we propose a boundary integral technique as a faster way to approximate gamma. This technique can also be used to calculate delta and theta. Our paper is the first to provide complete simulation-based approximations for all of the Greeks (delta, gamma, theta, rho, and vega) of American options. To make the computational process more efficient, we incorporate a Brownian Bridge into the numerical simulations. We then extend the application to American basket options.

Bio: P.A. Nguyen is a PhD candidate in the University of Minnesota's Industrial Systems Engineering (ISyE) Doctoral Program. She is working with Dr. Dan Mitchell whose focus is in the area of financial engineering, specifically applying stochastic control to problems in finance and quantitative risk management. P.A. is also an alumna of the Master of Financial Mathematics (MFM) at the University of Minnesota (2014) and is currently a teaching assistant for the MFM. She worked in enterprise risk management, primarily in credit risk and interest rate risk areas, for a few years before joining UMNs ISyE PhD program.

Fri Feb 15

## Lie Theory Seminar

3:35pm - Vincent Hall 313
Lie Theory Seminar
Lue Pan,, University of Chicago
Fri Feb 15

## Special Events and Seminars

3:35pm - Vincent Hall 313
Fontaine-Mazur conjecture in the residually reducible case (II)
Lue Pan, University of Chicago
##### Abstract:

We prove the modularity of some two-dimensional residually reducible p-adic Galois representations over Q when p is at least 5. In the first talk, I will present a generalization of Emerton's local-global compatibility result. In the second talk, I will use this compatibility result to make a patching argument for completed homology in this setting.

Fri Feb 15

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Plabic R-Matrices
Sunita Chepuri, University of Minnesoa
##### Abstract:

Postnikov's plabic graphs in a disk are used to parametrize totally positive Grassmannians. One of the key features of this theory is that if a plabic graph is reduced, the face weights can be uniquely recovered from boundary measurements. On surfaces more complicated than a disk this property is lost. In this talk, we investigate a certain semi-local transformation of weights for plabic networks on a cylinder that preserves boundary measurements. We call this a plabic R-matrix. We explore the properties of the plabic R-matrix, including the symmetric group action it induces on plabic networks and its underlying cluster algebra structure.

Fri Feb 15

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Feb 15

8:30am -
CANCELLED

Thu Feb 14

## Differential Geometry and Symplectic Topology Seminar

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

Thu Feb 14

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Feb 14

## Special Events and Seminars

1:25pm - Vincent Hall 113
Fontaine-Mazur conjecture in the residually reducible case (I)
Lue Pan, University of Chicago
##### Abstract:

We prove the modularity of some two-dimensional residually reducible p-adic Galois representations over Q when p is at least 5. In the first talk, I will present a generalization of Emerton's local-global compatibility result. In the second talk, I will use this compatibility result to make a patching argument for completed homology in this setting.

Thu Feb 14

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Feb 14

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Feb 14

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Feb 14

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Counting Number Fields, Second Order Asymptotics, and Hurwitz Spaces
Greg Michel, University of Minnesota
##### Abstract:

I'll introduce well-known counting conjectures related to number fields of bounded discriminants, and then I'll talk about some semi-related topological ideas that may allow us to strengthen these conjectures in certain situations.

Thu Feb 14

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570

Wed Feb 13

8:30pm - Vincent Hall 213
TBD
Wed Feb 13

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Indecomposable objects in Deligne's category Rep(S_t) - continuation
Peter Webb, University of Minnesota
##### Abstract:

We continue with Section 3 of the paper by Comes and Ostrik, On blocks of Deligne's category Rep(S_t). Section 3 begins with the result that the indecomposable objects are parametrized by partitions of all sizes, and this has to do with a description of the idempotents in the partition algebras. We use a fundamental relationship that goes back to Green, between idempotents an algebra, and idempotents in a factor algebra by an idempotent, and in the algebra obtained by cutting by that idempotent.

Wed Feb 13

## AMS Intro to Research Seminar

12:20pm - Vincent Hall 570
1st Annual AMS Sock Derangement
TBA
##### Abstract:

In combinatorics there is a classic problem about a "hat check," where patrons submit their hats, return slips are lost, and people get them back willy nilly. People get sad, angry, happy, you name it! In fact, as the number of people checking hats goes to infinity, the probability that NO ONE gets their hat back goes to 1/e! Well, here at the U of M math department, we are all about generalizations. Therefore, we present to you: The 1st annual AMS Sock Derangement! (a generalization of the AMS hat check)

Tue Feb 12

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Feb 12

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Feb 12

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Tue Feb 12

## PDE Seminar

10:00am - Vincent Hall 570
Global existence in incompressible fluid equations
Javier Gomez-Serrano, Princeton University
##### Abstract:

There has been high scientific interest to understand the behavior of the surface quasi-geostrophic (SQG) equation because it is a possible model to explain the formation of fronts of hot and cold air and because it also exhibits analogies with the 3D incompressible Euler equations. It is not known at this moment if this equation can produce singularities or if solutions exist globally. In this talk, I will discuss some recent works on the existence of global solutions for the SQG and modified SQG equations.

Mon Feb 11

## MCFAM Distinguished Lecture Series

5:30pm - Vincent Hall 16
Coding Capital: The Legal vs. The Digital Code
Katharina Pistor, Columbia Law School
##### Abstract:

In my forthcoming book, The Code of Capital: How Law Creates Wealth and Inequality, I argue that capital is coded in law, or more specifically in core institutions of private law, including property, collateral, trust, corporate, bankruptcy as well as contract law. These modules of the code of capital bestow critical attributes on simple assets, such as objects or claims, and there by transform them from simple into a wealth generating assets. These attributes are priority, durability, convertibility and universality, and critically, they depend on effective state backing. Recently, law has met a potential competitor in the form of the digital code. Blockchain and similar technologies, in particular, makes it possible to encode commitments such that they will be executed irrespective of a change of heart, or circumstances. Decentralized verification of resources and rights instead of ex post vindication of legal title promises a world without courts and without coercive law enforcement. In short, a new code may be on the horizon and its relation to the legacy, or legal, code raises fundamental questions about how to organize economic relations in an uncertain world and about who gets to set the parameters for doing so.

Bio: Katharina Pistor is the Edwin B. Parker Professor of Comparative Law at Columbia Law School and director of the Law Schools Center on Global Legal Transformation. Her research and teaching spans corporate law, corporate governance, money and finance, property rights, comparative law and law and development. She has published widely in legal and interdisciplinary journals and is the author can co-author of several books. She is the recipient of the Max Planck Research Award (2012) and of several grants by, among others the Institute for New Economic Thinking, and the National Science Foundation. Her most recent book, The Code of Capital: How the Law Creates Wealth and Inequality is forthcoming at Princeton University Press.

Mon Feb 11

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Integral representations of cuspidal-data Eisenstein series
Paul Garrett, University of Minnesota
Mon Feb 11

## PDE Seminar

3:35pm - Vincent Hall 313
Computer-Assisted Proofs in Partial Differential Equations
Javier Gomez-Serrano, Princeton University
##### Abstract:

In the last 50 years computing power has experienced an enormous development: every two years the number of transistors has doubled since the 1970s. However, even nowadays when we can perform very fast computations it is not clear a priori if one can obtain rigorous results based on the output of computer calculations. In this talk I will explain the basics of interval analysis and how it can be used to prove theorems in different contexts of PDE, ranging from fluid dynamics to spectral geometry.

Mon Feb 11

## Topology Seminar

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

Mon Feb 11

## Applied and Computational Mathematics Seminar

3:30pm - Vincent Hall 113
Applied and Computational Mathematics Seminar
Vera Andreeva rescheduled - February 18
Mon Feb 11

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Greg Shakhnarovich, Toyota Technological Institute at Chicago
Fri Feb 08

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Feb 08

## MCFAM Seminar

5:30pm - Vincent Hall 16
Today's Seminar - Canceled
Jie Ding, School of Statistics - University of Minnesota
##### Abstract:

In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are employed, a crucial step is to select the most appropriate model or method from a set of candidates. Model selection is a key ingredient in data analysis for reliable and reproducible statistical inference or prediction, and thus central to scientific studies in fields such as ecology, economics, engineering, finance, political science, biology, and epidemiology. There has been a long history of model selection techniques that arise from researches in statistics, information theory, and signal processing. A considerable number of methods have been proposed, following different philosophies and exhibiting varying performances. The purpose of this talk is to bring an overview of them, in terms of their motivation, large sample performance, and applicability. I will provide practically relevant discussions on theoretical properties of state-of- the-art model selection approaches, and share some thoughts on controversial views on the practice of model selection.

Fri Feb 08

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Whitney Numbers for Cones
Galen Dorpalen-Barry, University of Minnesota
##### Abstract:

An arrangement of hyperplanes dissects space into connected components called chambers. A nonempty intersection of halfspaces from the arrangement will be called a cone. The number of chambers of the arrangement lying within the cone is counted by a theorem of Zaslavsky, as a sum of certain nonnegative integers that we will call the cone's "Whitney numbers of the 1st kind". For cones inside the reflection arrangement of type A (the braid arrangement), cones correspond to posets, chambers in the cone correspond to linear extensions of the poset, and these Whitney numbers refine the number of linear extensions. We present some basic facts about these Whitney numbers, and interpret them for two families of poset

Fri Feb 08

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Feb 08

## Probability Seminar

2:30pm - Vincent Hall 213
Stability of the Bakry-Emery theorem on R^n
##### Abstract:

In R^n, the Bakry-Émery theorem states that the sharp constant in various functional inequalities for uniformly log-concave measures is no worse than the sharp constant for the Gaussian measure. As a consequence, uniformly log-concave measures inherit certain nice features of the Gaussian, like good measure concentration properties.

In this talk, I'll discuss quantitative stability estimates for the Bakry-Émery bound on logarithmic Sobolev and Poincaré constants. In particular, if a 1-uniformly log-concave measure has almost the same logarithmic Sobolev or Poincaré constant as the standard Gaussian measure, then it must (almost) split off a Gaussian factor. As a corollary, we obtain dimension-free stability estimates for Gaussian concentration of Lipschitz functions. The proofs combine Steins method, optimal transport, and simple variational arguments.

Joint work with Max Fathi.

Fri Feb 08

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Karyn Sutton, The Institute for Disease Modeling
Fri Feb 08

8:30am -
CANCELLED

Thu Feb 07

## Differential Geometry and Symplectic Topology Seminar

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

Thu Feb 07

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Feb 07

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Feb 07

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Feb 07

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Feb 07

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Thu Feb 07

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570

Wed Feb 06

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Indecomposable objects in Deligne's category Rep(S_t)
Peter Webb, University of Minnesota
##### Abstract:

We will start on Section 3 of the paper by Comes and Ostrik, On blocks of Deligne's category Rep(S_t). This will be preceded by a review of the set-up in this category, which is built up out of partition algebras. Section 3 begins with the result that the indecomposable objects are parametrized by partitions of all sizes.

Tue Feb 05

## Colloquium

3:35pm - Vincent Hall 16
A Multiscale/Multiphysics Coupling Framework for Heart Valve Damage
Yue Yu, Lehigh University
##### Abstract:

Bioprosthetic heart valves (BHVs) are the most popular artificial replacements for diseased valves that mimic the structure of native valves. However, the life span of BHVs remains limited to 10-15 years, and the mechanisms that underlie BHVs failure remain poorly understood. Therefore, developing a unifying mathematical framework which captures material damage phenomena in the fluid-structure interaction environment would be extremely valuable for studying BHVs failure. Specifically, in this framework the computational domain is composed of three subregions: the fluid (blood) , the fracture structure (damaged BHVs) modeled by the recently developed nonlocal (peridynamics) theory, and the undamaged thin structure (undamaged BHVs). These three subregions are numerically coupled to each other with proper interface boundary conditions.

In this talk, I will introduce two sub-problems and the corresponding numerical methods we have developed for this multiscale/multiphysics framework. In the first problem the coupling strategy for fluid and thin structure is investigated. This problem presents unique challenge due to the large deformation of BHV leaflets, which causes dramatic changes in the fluid subdomain geometry and difficulties on the traditional conforming coupling methods. To overcome the challenge, the immersogeometric method was developed where the fluid and thin structure are discretized separately and coupled through penalty forces. To ensure the capability of the developed method in modeling BHVs, we have verified and validated this method. The second problem focuses on the nonlocal Neumann-type interface boundary condition which plays a critical role in the fluidperidynamics coupling framework. In the nonlocal models the Neumann-type boundary conditions should be defined in a nonlocal way, namely, on a region with non-zero volume outside the surface, while in fluidstructure interfaces the hydrodynamic loadings from the fluid side are typically provided on a sharp co-dimensional one surface. To overcome this challenge, we have proposed a new nonlocal Neumann-type boundary condition which provides an approximation of physical boundary conditions on a sharp surface, with an optimal asymptotic convergence rate to the local counter part. Based on this new boundary condition, we have developed a fluidperidynamics coupling framework without overlapping regions.

Tue Feb 05

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Feb 05

## Math Physics Seminar

12:20pm - Vincent Hall 209
Choreography in 3-body Classical Mechanics
Sasha Turbiner, ICN-UNAM, Mexico
##### Abstract:

By definition the choreography (dancing curve) is the trajectory
on which n classical bodies move chasing each other without collisions
with equal time delay. The first choreography (the remarkable Figure Eight)
at zero angular momentum was discovered unexpectedly by C Moore
(Santa Fe Institute) in 1993 for 3 equal masses in R^3 Newtonian gravity, numerically
and rigorously confirmed by Chenciner-Montgomery (2000). At the moment
about 6,000 choreographies are known, all numerically, in Newtonian gravity.
Possibly all known dancing curves are non-algebraic.

Does there exist (non)-Newtonian gravity for which the dancing curve is known
analytically? - Yes, a single example is known - it is the algebraic
lemniscate by Jacob Bernoulli (1694) - and it will be a concrete subject of the talk. Astonishingly, Newtonian Figure Eight coincides with algebraic lemniscate with
\chi^2 deviation 10^{-7}. Both choreographies admit any odd numbers of bodies
on them. 3-body choreography on algebraic lemniscate defines maximally
superintegrable trajectory with seven constants of motion and, possible,
polynomial algebra of integrals.

Tue Feb 05

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Feb 04

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory
Postponed
Mon Feb 04

## Topology Seminar

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

Mon Feb 04

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Tom Needham, The Ohio State University
Fri Feb 01

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Feb 01

## MCFAM Seminar

5:30pm - Vincent Hall 16
Computational Issues in Making Math Models Operational in Insurance
Scott Monitor, VP & Financial Engineer - MFM alumnus, FSA
##### Abstract:

Many insurance companies offer a wide array of investment guarantees, and some of these are complicated and have no clear analytical solution. In order to manage these contracts and along with increased scrutiny from regulatory bodies, companies are having to value these contracts more frequently and in a greater number of runs. We will demonstrate methodologies and computational approaches to be able to perform analysis on these contract that can be actionable and timely.

Fri Feb 01

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Enumerating Linear Systems on Graphs
David Perkinson, Reed College
##### Abstract:

To play the dollar game on a graph, start by assigning to each vertex a number of dollars of either wealth or debt. From this initial state, called a "divisor", the vertices lend and borrow with their neighbors according to chip-firing rules in an attempt to reach a debt-free state. The set of all possible winning states is the "complete linear system" of the divisor. We are interested in determining its cardinality. In the figure below, each vertex represents one of the 201 winning positions resulting from giving ten dollars to one vertex of the cycle graph on five vertices. This is joint work with Sarah Brauner and Forrest Glebe.

Fri Feb 01

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Feb 01

## Probability Seminar

2:30pm - Vincent Hall 213
Nonequilibrium particle systems in inhomogeneous space
Leonid Petrov, University of Virginia
##### Abstract:

I will discuss stochastic interacting particle systems in the Kardar-Parisi-Zhang universality class evolving in one-dimensional inhomogeneous space. The inhomogeneity means that the speed of a particle depends on its location. I will focus on integrable cases, i.e., for which certain observables can be written in an exact form suitable for asymptotic analysis. Examples include a new continuous-space version of TASEP (totally asymmetric simple exclusion process), and the pushTASEP (=long-range TASEP). For integrable systems, limit shapes of particles density can be described in an explicit way. Asymptotics of fluctuations around infinite traffic jams, also available explicitly, bring phase transitions of a novel nature.

Fri Feb 01

8:30am -
CANCELLED

Thu Jan 31

## Colloquium

3:35pm - Vincent Hall 16
From infinite random matrices over finite fields to square ice
Leonid Petrov, University of Virginia
##### Abstract:

Asymptotic representation theory of symmetric groups is a rich and beautiful subject with deep connections with probability, mathematical physics, and algebraic combinatorics. A one-parameter deformation of this theory related to infinite random matrices over a finite field leads to randomization of the classical Robinson-Schensted correspondence between words and Young tableaux. Exploring such randomizations we find unexpected applications to six vertex (square ice) type models and traffic systems on a 1-dimensional lattice.

Thu Jan 31

## Differential Geometry and Symplectic Topology Seminar

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

Thu Jan 31

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Jan 31

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Jan 31

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Jan 31

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Jan 31

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Thu Jan 31

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570

Wed Jan 30

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Postponed to next week
Peter Webb, University of Minnesota
##### Abstract:

We will start on Section 3 of the paper by Comes and Ostrik, On blocks of Deligne's category Rep(S_t). This will be preceded by a review of the set-up in this category, which is built up out of partition algebras. Section 3 begins with the result that the indecomposable objects are parametrized by partitions of all sizes.

Tue Jan 29

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Jan 29

## Math Physics Seminar

12:20pm - Vincent Hall 209
Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras
Ian Marqutte, University of Queensland
##### Abstract:

I will review results on classification of quantum superintegrable systems on two-dimensional Euclidean space allowing separation of variables in Cartesian coordinates and possessing an extra integral of third or fourth order. The exotic quantum potential satisfy a nonlinear ODE and have been shown to exhibit the Painleve property. I will also present different constructions of higher order superintegrable Hamiltonians involving Painleve transcendents using four types of building blocks which consist of 1D Hamiltonians allowing operators of the type Abelian, Heisenberg, Conformal or Ladder. Their integrals generate finitely generated polynomial algebras and representations can be exploited to calculate the energy spectrum. I will point out that for certain cases associated with exceptional orthogonal polynomials, these algebraic structures do not allow to calculate the full spectrum and degeneracies. I will describe how other sets of integrals can be build and used to provide a complete solution.

Tue Jan 29

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Jan 28

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory
Postponed
Mon Jan 28

## Topology Seminar

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

Mon Jan 28

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Guanglin Xu, University of Minnesota, Twin Cities
Fri Jan 25

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA, TBA
Fri Jan 25

## MCFAM Seminar

5:30pm - Vincent Hall 16
No MCFAM Seminar

Fri Jan 25

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Jan 25

## Probability Seminar

2:30pm - Vincent Hall 213
Large deviations for sparse random graphs
Nicholas Cook, Stanford University
##### Abstract:

Let $G=G(N,p)$ be an Erd\H{o}s--R\'enyi graph on $N$ vertices (where each pair is connected by an edge independently with probability $p$). We view $N$ as going to infinity, with $p$ possibly going to zero with $N$. What is the probability that $G$ contains twice as many triangles as we would expect? I will discuss recent progress on this infamous upper tail" problem, and more generally on tail estimates for counts of any fixed subgraph. These problems serve as a test bed for the emerging theory of \emph{nonlinear large deviations}, and also connect with issues in extending the theory of \emph{graph limits} to handle sparse graphs. In particular, I will discuss our approach to the upper tail problems via new versions of the classic regularity and counting lemmas from extremal combinatorics, specially tailored to the study of random graphs in the large deviations regime. This talk is based on joint work with Amir Dembo.

Fri Jan 25

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Eric Lind, Metro Transit
Fri Jan 25

8:30am -
CANCELLED

Thu Jan 24

## Differential Geometry and Symplectic Topology Seminar

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

Thu Jan 24

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Jan 24

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Jan 24

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Jan 24

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Thu Jan 24

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570

Tue Jan 22

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Jan 22

## Colloquium

2:30pm - Vincent Hall 16
Multiscale Problems in Cell Biology
Chuan Xue, Ohio State University
##### Abstract:

Complex biological systems involve multiple space and time scales. To get an integrated understanding of these systems involves multiscale modeling, computation and analysis. In this talk, I will discuss two such examples in cell biology and illustrate how to use multiscale methods to explain experimental data. The first example is on chemotaxis of bacterial populations. I will present recent progress on embedding information of single cell dynamics into models of cell population dynamics. I will clarify the scope of validity of the well-known Patlak-Keller-Segel chemotaxis equation and discuss alternative models when it breaks down. The second example is on the axonal cytoskeleton dynamics in health and disease. I will present a stochastic multiscale model that gave the first mechanistic explanation for the cytoskeleton segregation phenomena observed in many neurodegenerative diseases.

Tue Jan 22

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Jan 22

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Jan 21

## Topology Seminar

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

Fri Jan 18

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Jan 18

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Jan 18

8:30am -
CANCELLED

Thu Jan 17

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Jan 15

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Jan 14

## Topology Seminar

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

Fri Jan 11

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Jan 11

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Jan 11

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Jan 11

8:30am -
CANCELLED

Thu Jan 10

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Jan 08

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Jan 07

## Topology Seminar

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

Fri Jan 04

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Jan 04

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Jan 04

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Jan 04

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Jan 04

8:30am -
CANCELLED

Thu Jan 03

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Jan 01

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Dec 31

## Topology Seminar

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

Fri Dec 28

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Dec 28

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Dec 28

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Dec 28

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Dec 28

8:30am -
CANCELLED

Thu Dec 27

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Dec 25

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Dec 24

## Topology Seminar

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

Fri Dec 21

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Dec 21

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Dec 21

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Dec 21

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Dec 21

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Dec 21

8:30am -
CANCELLED

Thu Dec 20

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Dec 20

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Projective Geometry, Complex Hyperbolic Space, and Geometric Transitions
Steve Trettel, UC Santa Barbara
##### Abstract:

The natural analog of Teichmuller theory for hyperbolic manifolds in dimension 3 or greater is trivialized by Mostow Rigidity, so mathematicians have worked to understand more general deformations. Two well studied examples, convex real projective structures and complex hyperbolic structures, have been investigated extensively and provide independently developed deformation theories. Here we will discuss a surprising connection between the these, and construct a one parameter family of geometries deforming complex hyperbolic space into a new geometry built out of real projective space and its dual. This connects the aforementioned deformation theories and provides geometric motivation for a representation-theoretic observation of Cooper, Long, and Thistlethwaite

Thu Dec 20

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Dec 20

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Dec 20

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA
Thu Dec 20

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Dec 19

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Dec 18

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Dec 18

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Dec 18

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Dec 17

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Forms and Number Theory

Mon Dec 17

## Applied and Computational Math Colloquium

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

Mon Dec 17

## Topology Seminar

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

Mon Dec 17

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Dec 17

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Dec 14

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Dec 14

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Dec 14

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Dec 14

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Dec 14

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Dec 14

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Dec 14

8:30am -
CANCELLED

Thu Dec 13

## Student Combinatorics Seminar

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

Thu Dec 13

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Dec 13

## Differential Geometry and Symplectic Topology Seminar

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

Thu Dec 13

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Dec 13

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Dec 13

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Galois Representations and the Modularity Theorem
Andy Hardt, University of Minnesota
##### Abstract:

I will continue Katy's talk from last week, and talk about chapter 9 of Diamond and Shurman's "A First Course in Modular Forms." We'll define Galois representations corresponding to both elliptic curves and modular forms. Then we'll state the modularity theorem, which asserts that every elliptic curve corresponds to a modular form, and their Galois representations are equal. If we have time, we'll relate this back to the version of the theorem from last week, which equated points on an elliptic curve to Fourier coefficients of a modular form. The proof of the theorem, however, will be left as an exercise to the listener.

Thu Dec 13

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Dec 12

## PDE Seminar

3:35pm - Vincent Hall 570
Scattering for the 3D Gross-Pitaevskii equation
Zihua Guo, Monash University
##### Abstract:

We study the Cauchy problem for the 3D Gross-Pitaevskii equation. Global well-posedness in the natural energy space was proved by Gerard.
We prove scattering for small data in the same space with some additional angular regularity, and in particular in the radial case we obtain small energy scattering.
The crucial ingredients are new generalized Strichartz estimates and some new observed "NULL" structures of the Gross-Pitaevskii equation after some normal form type transform.
This is a joint work with Zaher Hani and Kenji Nakanishi.

Tue Dec 11

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Dec 11

## Math Physics Seminar

12:20pm - Vincent Hall 313
Application of Invariant Signatures: Solving Jigsaw Puzzles
Rob Thompson
Tue Dec 11

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Dec 11

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Dec 10

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Forms and Number Theory

Mon Dec 10

## Applied and Computational Math Colloquium

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

Mon Dec 10

## Special Events and Seminars

3:35pm - Vincent Hall 207
Optimal transport on graphs with Applications
Wuchen Li
##### Abstract:

In recent years, optimal transport has many applications in evolutionary dynamics, statistics, and machine learning. In this talk, we introduce dynamical optimal transport on finite graphs. We proposed to study the probability simplex as a Riemannian manifold with a Wasserstein metric. We call it a probability manifold. Various developments, especially the Fokker-Planck equation, will be introduced. The entropy production on graphs related to Shannon entropy will be established. Its connection with Fisher information and Yanos formula will be studied. Many examples, including Mean field games, geometry of graphs, statistical learning problems, will be presented.

Mon Dec 10

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: The geometric average size of Selmer groups over function fields
Aaron Landesman, Stanford
##### Abstract:

We use topological methods to investigate the average size of n-Selmer groups of elliptic curves over F_q(t).
Loosely speaking, the n-Selmer group of an elliptic curve measures objects which look like the n-torsion of the elliptic curve.
We relate the question of computing the average size of the n-Selmer group to demonstrating
homological stability for a sequence of moduli spaces
of these n-Selmer elements.
Via monodromy arguments, we show the number of components of these moduli spaces stabilizes, which determines the
average size after taking a large q limit.

Mon Dec 10

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Dec 10

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Stratifying High-Dimensional Data Based on Proximity to the Convex Hull Boundary
Lori Ziegelmeier, Macalester College
##### Abstract:

The convex hull of a set of points,C, serves to expose extremal properties of C and can help identify elements in C of high interest. For many problems, particularly in the presence of noise, the true vertex set (and facets) may be difficult to determine. One solution is to expand the list of high interest candidates to points lying near the boundary of the convex hull. We propose a quadratic program for the purpose of stratifying points in a data cloud based on proximity to the boundary of the convex hull. For each data point, a quadratic program is solved to determine an associated weight vector. We show that the weight vector encodes geometric information concerning the points relationship to the boundary of the convex hull. The computation of the weight vectors can be carried out in parallel, and for a fixed number of points and fixed neighborhood size, the overall computational complexity of the algorithm grows linearly with dimension. As a consequence, meaningful computations can be completed on reasonably large, high-dimensional data sets.

Lori Ziegelmeier received an A.S. and A.A. from Colby Community College in 2005. She completed her B.S. in Mathematics and B.A. in Liberal Arts and History, M.S. in Mathematics, and Ph.D. in Mathematics all at Colorado State University in 2007, 2009, and 2013, respectively. Since completing her doctoral degree, she has been in the Department of Mathematics, Statistics, and Computer Science at Macalester College and is currently an Assistant Professor. Her research is in the area of geometric and topological data analysis.

Mon Dec 10

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Dec 07

## MCFAM Seminar

5:30pm - Vincent Hall 16
Data Visualization in R
Chen Zhang, Sr. Consultant, Analytics & Research at Travelers; Ph.D. in Statistics from UConn; UMN MFM Alumnus
##### Abstract:

Data visualization is often overlooked by people working with data and/or modeling but can in fact reveal very useful insight into problems at hand. R is an open-source programming language for statistical computing and graphics with increasing popularity among practitioners in data science and machine learning in recent years. The "ggplot2" package in R, in particular, provides very powerful, intuitive and versatile tools for data visualization. An overview of these tools will be presented in this talk accompanied by a live demo.

Fri Dec 07

## Lie Theory Seminar

3:35pm - Vincent Hall 313
Finiteness of Frobenius traces of a de Rham local system
Koji Shimizu, University of California, Berkeley
##### Abstract:

Every smooth projective variety over a number field yields a Galois representation via etale cohomology, and the Weil conjecture tells that its Frobenius traces are integers. Fontaine and Mazur conjectured that Galois representations satisfying a local condition (de Rham) arise from geometry and hence have a similar finiteness property. In this talk, I will focus on de Rham local systems on algebraic varieties and explain a finiteness of Frobenius traces follows from the Fontaine-Mazur conjecture for Galois representations and the generalized Riemann Hypothesis

Fri Dec 07

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Catalan Functions and k-Schur functions
Anna Pun, Drexel University
##### Abstract:

Li-Chung Chen and Mark Haiman studied a family of symmetric functions called Catalan (symmetric) functions which are indexed by pairs consisting of a partition contained in the staircase (n-1, ..., 1,0) (of which there are Catalan many) and a composition weight of length n. They include the Schur functions, the Hall-Littlewood polynomials and their parabolic generalizations. They can be defined by a Demazure-operator formula, and are equal to GL-equivariant Euler characteristics of vector bundles on the flag variety by the Borel-Weil-Bott theorem. We have discovered various properties of Catalan functions, providing a new insight on the existing theorems and conjectures inspired by Macdonald positivity conjecture. A key discovery in our work is an elegant set of ideals of roots that the associated Catalan functions are k-Schur functions and proved that graded k-Schur functions are G-equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We exposed a new shift invariance property of the graded k-Schur functions and resolved the Schur positivity and k-branching conjectures by providing direct combinatorial formulas using strong marked tableaux. We conjectured that Catalan functions with a partition weight are k-Schur positive which strengthens the Schur positivity of Catalan function conjecture by Chen-Haiman and resolved the conjecture with positive combinatorial formulas in cases which capture and refine a variety of problems. This is joint work with Jonah Blasiak, Jennifer Morse and Daniel Summers.

Fri Dec 07

## Topology Seminar

3:30pm - 301 Vincent Hall
Topology Seminar: Power operations in normed motivic spectra
Tom Bachmann, MIT
##### Abstract:

In joint work with M. Hoyois, we established (the beginnings of) a theory of "normed motivic spectra". These are motivic spectra with some extra structure, enhancing the standard notion of a motivic E_oo-ring spectrum (this is similar to the notion of G-commutative ring spectra in equivariant stable homotopy theory). It was clear from the beginning that the homotopy groups of such normed spectra afford interesting *power operations*. In ongoing joint work with E. Elmanto and J. Heller, we attempt to establish a theory of these operations and exploit them calculationally. I will report on this, and more specifically on our proof of a weak motivic analog of the following classical result of Würgler: any (homotopy) ring spectrum with 2=0 is generalized Eilenberg-MacLane.

Fri Dec 07

## Probability Seminar

2:30pm - Vincent Hall 209
When particle systems meet PDEs
Li-Cheng Tsai, Columbia University
##### Abstract:

Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three paradigmatic facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.

Fri Dec 07

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Dec 07

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
The definition of Deligne's category Rep(S_t) - continuation
Cecily Santiago, University of Minnesota
##### Abstract:

We will complete the steps in the definition of Deligne's category described in section 2.2 of the paper, On blocks of Deligne's category Rep(S_t), by Comes and Ostrik.

Fri Dec 07

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
When Seeing is not Believing: New Forensics Algorithms to Detect Image Manipulations
Michael Albright, Honeywell
##### Abstract:

Modern image editing software has made it possible to alter images in ways that can dramatically change the image content, yet the images may appear authentic to humans. While there are countless beneficial applications of photo editing, image manipulations can also be used in harmful ways  e.g., altered images may be published to cause reputational harm, sway public opinions, influence elections, etc. Furthermore, with the growing popularity of social media and online sharing platforms, it is increasingly easy for altered media to go viral. Whats more, recent breakthroughs in artificial intelligence (AI) are making it dramatically easier to produce altered images, and even altered videos, that appear photo realistic. Hence, there is growing interest in developing new forensic methods that can detect manipulations in images and video. In this talk, I will give an overview of my teams work on the DARPA-funded Media Forensics (MediFor) Project to develop novel machine-learning algorithms for automated detection and localization of media manipulations.

Michael Albright is a senior data scientist in the Data Science and Video Analytics group in Honeywell Labs in Golden Valley, Minnesota. Since joining Honeywell in 2015, he has invented new technologies that solve challenging problems for internal Honeywell businesses and external customers. His work has involved applying machine learning, optimization, and other applied math and computer science techniques to a variety of problems in domains ranging from Internet of Things (IoT) systems to computer vision applications. Michael earned a Ph.D. in theoretical physics from the University of Minnesota in 2015 and has previous industry experience at Cray, Inc.

Fri Dec 07

## MathCEP Seminar

10:10am - Vincent Hall 364
Experiments in STEM Education
Michelle Driessen, University of Minnesota
##### Abstract:

The general chemistry program has been experimenting with several new pedagogies in order to improve student learning and successful outcomes. Ill begin with our placement system and new adaptive courseware/learning analytics project, and will discuss any other project as time allows.

1. ALEKS Placement/Learning Modules
Using Adaptivity and Learning Analytics to Identify At-Risk Students and Implement Early Interventions
Six Lower-Stakes Exams + Final
E-proctored Exams  available over a 12 hour window

Fri Dec 07

8:30am -
CANCELLED

Thu Dec 06

## Student Combinatorics Seminar

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

Thu Dec 06

## Colloquium

3:35pm - Vincent Hall 16
Number theory over function fields and geometry
Will Sawin, Columbia University
##### Abstract:

The function field model involves taking problems in
classical analytic number theory and replacing the integers with
polynomials over a finite field. This preserves most of the complexity
of these problems while giving them a stronger relationship to
geometry, allowing new techniques to be applied. We will explain how
this works using a recent example involving sums of the divisor
function where, thanks to good luck, particularly simple methods can
prove a particularly powerful result.

Thu Dec 06

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Enumerative geometry: old and new
Felix Janda, University of Michigan
##### Abstract:

For as long as people have studied geometry, they have counted
geometric objects. For example, Euclid's Elements starts with the
postulate that there is exactly one line passing through two distinct
points in the plane. Since then, the kinds of counting problems we are
able to pose and to answer has grown. Today enumerative geometry is a
rich subject with connections to many fields, including combinatorics,
physics, representation theory, number theory and integrable systems.

In this talk, I will show how to solve several classical counting
questions. Then I will describe a more modern problem with roots in
string theory which has been the subject of intense study for the last
two decades, namely the study of the Gromov-Witten invariants of the
quintic threefold, a Calabi-Yau manifold. I will explain a recent
break-through in understanding the higher genus invariants that stems
from a seemingly unrelated problem related to the study of holomorphic
differentials on Riemann surfaces.

Thu Dec 06

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Dec 06

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
A Tour of the Modularity Theorem
Katy Weber, University of Minnesota
##### Abstract:

The Modularity Theorem (also known as the Taniyama-Shimura-Weil Conjecture) states, essentially, that every elliptic curve arises from a modular form. It is a special case of the Langlands correspondence and was a major part of Andrew Wiles' proof of Fermat's Last Theorem. In this talk, I will sketchily discuss the theorem in its various forms, leading up to the statement that the L-function of an elliptic curve agrees with the L-function of a modular form. Along the way, we will encounter some algebraic geometry words, e.g. "moduli space," "universal curve," and "sheaf."

Thu Dec 06

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Dec 06

## Climate Seminar

11:15am - Vincent Hall 570
Stability of traveling pulses in the FitzHugh--Nagumo equations
Paul Carter, University of Arizona
##### Abstract:

Traveling waves arise in partial differential equations in a broad range of applications, for instance chemical reactions, propagation of electrical signals, or the dynamics of traffic jams. The notion of stability of a traveling wave solution concerns its resilience to small perturbations and can usually be inferred from an eigenvalue problem obtained by linearizing the PDE about the solution. In this talk, I will discuss these ideas in the context of the FitzHugh--Nagumo system, a simplified model of nerve impulse propagation. I will present existence and stability results for (multi)pulse solutions, and I will describe a phenomenon whereby unstable eigenvalues accumulate as a single pulse is continuously deformed into a double pulse

Thu Dec 06

## Special Events and Seminars

11:00am - Tate Hall B20
Koji Shimizu, University of California, Berkeley
##### Abstract:

An etale p-adic local system on a rigid analytic variety can be regarded as a family of p-adic Galois representations parametrized by the variety, and p-adic Hodge theory has brought many results and applications on such objects, including a p-adic Riemann-Hilbert correspondence by Diao, Lan, Liu and Zhu. I will discuss constancy of a key invariant (generalized Hodge-Tate weights) of general p-adic local systems

Wed Dec 05

## PDE Seminar

3:35pm - Vincent Hall 570
Barotropic instability of shear flows
Zhiwu Lin, Georgia Institute of Technology
##### Abstract:

We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop an approach by using the Hamiltonian structures of the linearized equation and an instability index formula to find the sharp stability conditions. We studied the flow with Sinus profile in details and found the sharp stability boundary in the whole parameter space, which corrected previous results in the fluid literature. The addition of the Coriolis force brings some fundamental changes to the stability of shear flows. Moreover, we also study the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping near the shear flows. This is joint work with Hao Zhu and Jincheng Yang.

Tue Dec 04

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Dec 04

## Math Physics Seminar

12:20pm - Vincent Hall 313
Revivals and Fractalization in the Linear Free Space Schrödinger Equation with Pseudoperiodic Boundary Conditions
Natalie Sheils
##### Abstract:

We consider the one-dimensional linear free space Schrödinger equation on a bounded interval subject to homogeneous linear boundary conditions. We prove that, in the case of pseudoperiodic boundary conditions, the solution of the initial-boundary value problem exhibits the phenomenon of revival at specific ("rational'') times, meaning that it is a linear combination of a certain number of copies of the initial datum. Equivalently, the fundamental solution at these times is a finite linear combination of delta functions. At other ("irrational'') times, for suitably rough initial data, e.g., a step or more general piecewise constant function, the solution exhibits a continuous but fractal-like profile. Further, we express the solution for general homogeneous linear boundary conditions in terms of numerically computable eigenfunctions. (Joint work with Peter Olver and David Smith)

Tue Dec 04

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Dec 04

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Dec 03

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
A Chebotarev density theorem for families of fields with an application to bounding l-torsion in class groups
Caroline Turnage-Butterbaugh
Mon Dec 03

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Interfaces with singularities: understanding phase transitions in nematic liquid crystals
Dmitry Golovaty, Department of Mathematics, University of Akron
##### Abstract:

A nematic liquid crystal is essentially a liquid that exhibits some orientational order. The liquid crystalline state is typically observed in materials composed of highly asymmetric molecules for temperatures in the intermediate range when the material is neither a classical liquid nor a solid. In this talk we will be interested in describing a phase transition between the nematic and the isotopic state when the nematic order melts and the liquid crystal turns into a regular isotopic fluid. The experimental observations of this process indicate that the transition proceeds via evolution of interfaces separating different phases where the interfaces are generally not smooth. Our goal in this talk is to explain presence of these phase boundary singularities from a mathematical point of view .

The nematic-to-isotopic phase transition can be described within the so called Landau-de Genes variational theory for a tensor-valued order parameter. Because this theory is rather complex, in order to develop an initial understanding of transitions between the ordered and disordered states, we propose a simpler toy model based on the modified Ginzburg-Landau-type energy defined over vector fields on the plane. The corresponding variational model consists of anisotropic gradient terms and a potential that vanishes on two disconnected sets. While this model may not quantitatively describe the nematic state, the topology of the simplified target set retains the crucial features of the full problem. The principal observation from the study of the simplified model is that the phase boundary singularities can be explained by large disparity between the elastic constants that specify the gradient contribution to the energy. In the talk we will present a combination of rigorous analysis and numerics that leads to this conclusion.

Mon Dec 03

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Dec 03

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 30

## MCFAM Seminar

5:30pm - Vincent Hall 16
The Effect of the Risk Corridors Program on Marketplace Premiums and Participation
Pinar Karaca Mandic, MILI Director/Carlson Finance Professor
##### Abstract:

We investigate the effect of the Risk Corridors (RC) program
on premiums and insurer participation in the Affordable Care Act
(ACA)s Health Insurance Marketplaces. The RC program, which was
defunded ahead of coverage year 2016, and ended in 2017, is a risk
sharing mechanism: it makes payments to insurers whose costs are high
relative to their revenue, and collects payments from insurers whose
costs are relatively low. We show theoretically that the RC program
creates strong incentives to lower premiums for some insurers.
Empirically, we find that insurers who claimed RC payments in 2015,
program ended. Insurance markets in which more insurers made RC claims
experienced larger premium increases after the program ended,
reflecting equilibrium effects. We do not find robust evidence that
insurers with larger RC claims in 2015 were less likely to participate
in the ACA Marketplaces in 2016 and 2017. Overall we find that the end
of the RC program significantly contributed to premium growth.

Fri Nov 30

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Grassmann Pentagram Maps and Non-commutative Integrable Systems
Nicholas Ovenhouse, Michigan State University
##### Abstract:

The pentagram map is a discrete dynamical system on the space of plane polygons. Gekhtman, Shapiro, Tabachnikov, and Vainshtein used the combinatorics and Poisson geometry associated to certain networks/quivers on surfaces to prove that this map is integrable. Recently, Mari-Beffa and Felipe introduced a version of the pentagram map on Grassmannians, and found a Lax representation. I will generalize the techniques of Gekhtman et. al. to the Grassmann case, and show this gives a "formal" integrable system in a non-commutative algebra.

Fri Nov 30

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Nov 30

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Nov 30

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 30

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
The definition of Deligne's category Rep(S_t)
Cecily Santiago, University of Minnesota
##### Abstract:

Following section 2.2 of the paper, On blocks of Deligne's category Rep(S_t), by Comes and Ostrik, we give the definition of this category and explore some of its first properties.

Fri Nov 30

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Recap of MinneMUDAC: Challenges and Improvements
-, -
##### Abstract:

Graduate-level participants of 2018 MinneMUDAC data challenge will give an updated version of their original presentation, supplemented with suggestions for potential improvements to answering the challenge question, which was predicting the voter turnout for the 2018 midterm elections in Minnesota. After the talks, all participants will break into discussions regarding the presentations and the questions that arise from them.

Speakers: Several teams that competed in MinneMUDAC

Fri Nov 30

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Nov 30

8:30am -
CANCELLED

Thu Nov 29

## Student Combinatorics Seminar

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

Thu Nov 29

## Colloquium

3:35pm - Vincent Hall 16
Interpolative decomposition and its applications
Lexing Ying, Stanford, Ordway Visitor
##### Abstract:

Interpolative decomposition is a simple and yet powerful tool for approximating low-rank matrices. After discussing the theory and algorithm, I will present a few new applications of interpolative decomposition in numerical partial differential equations, quantum chemistry, and machine learning.

Thu Nov 29

## IMA Data Science Lab Seminar

3:35pm - Vincent 16
Interpolative Decomposition and its Applications (Math Dept Colloquium Lecture)
Lexing Ying, Stanford University
##### Abstract:

Interpolative decomposition is a simple and yet powerful tool for approximating low-rank matrices. After discussing the theory and algorithm, I will present a few new applications of interpolative decomposition in numerical partial differential equations, quantum chemistry, and machine learning.

Thu Nov 29

## Differential Geometry and Symplectic Topology Seminar

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

Thu Nov 29

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
On invariant theory for "coincidental" reflection groups
Victor Reiner, University of Minnesota
##### Abstract:

(joint work with A. Shepler and E. Sommers)
Complex reflection groups W are the finite subgroups of GL_n(C) with the following property: when they act on polynomials in n variables, their invariant ring is again a polynomial algebra. It is also known by
a result of Eagon and Hochster that, for any of their W-representations U, the U-isotypic polynomials form a _free_ module over the W-invariant subalgebra. In a few cases, we know an explicit basis for these U-isotypic polynomials. This talk will discuss a class of complex reflection groups W, sometimes called the "coincidental types", where conjecturally we know explicit bases for the U-isotypic component when U is any tensor product of the exterior powers of the reflection representation and its dual. This conjecture would explain pleasant product formulas for combinatorial objects, such as face numbers for finite type cluster complexes.

Thu Nov 29

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
The Weil Conjectures: 0 to 100
Liam Keenan, University of Minnesota
##### Abstract:

The Weil conjectures are perhaps one of the most stunning achievements in arithmetic geometry in the 20th century. In this talk, I plan to introduce the necessary algebro-geometric language, state the conjectures, discuss the some of the tools used to prove them, and draw connections to analytic number theory.

Thu Nov 29

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 29

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Thu Nov 29

## Colloquium

10:00am - Vincent Hall 570
The role of Energy in Regularity
Max Engelstein, MIT
##### Abstract:

The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy.

However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field.

We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur

Wed Nov 28

## PDE Seminar

3:30pm - Vincent Hall 570
An Epiperimetric Approach to Isolated Singularities
Max Engelstein, MIT
##### Abstract:

The presence of singular points (i.e. points around which the object in question does not look flat at any scale) is inevitable in most minimization problems. One fundamental question is whether minimizers have a unique tangent object at singular points i.e., is the minimizer increasingly well approximated by some other minimizing object as we zoom in at a singular point. This question has been investigated with varying degrees of success in the settings of minimal surfaces, harmonic maps and obstacle problems amongst others.

In this talk, we will give the first uniqueness of blowups result for minimizers of the Alt-Caffarelli functional. In particular, we prove that the tangent object is unique at isolated singular points in the free boundary. Our main tool is a new approach to proving (log-)epiperimetric inequalities at isolated singularities. This epiperimetric inequality differs from previous ones in that it holds without any additional assumptions on the symmetries of the tangent object.

If we have time, we will also discuss how this method allows us to recover some uniqueness of blow-ups results in the minimal surfaces setting, particularly those of Allard-Almgren (81) and Leon Simon (83). This is joint work with Luca Spolaor (MIT) and Bozhidar Velichkov (U. Grenoble Alpes).

Wed Nov 28

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Convex Relaxation Approaches for Strictly Correlated Density Functional Theory
Lexing Ying, Stanford University
##### Abstract:

In this talk, we introduce methods from convex optimization to solve the multi-marginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of N-representable 2-marginals and 3-marginals, which in turn provide lower bounds to the energy. We further propose rounding schemes to obtain upper bound to the energy.

Tue Nov 27

## Colloquium

3:35pm - Vincent Hall 16
Surface bundles, monodromy, and arithmetic groups
Bena Tshishiku, Harvard University
##### Abstract:

Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to "compute" (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter.

Tue Nov 27

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar - Eddie Nijholt - Cancelled
Eddie Nijholt, UIUC
##### Abstract:

Network dynamical systems play an important role in many fields of science; whenever there are agents whose time evolution is linked through some interaction structure, we may view the system as a network and model it accordingly. However, despite their prevalence, network dynamical systems are in general not well understood. One can identify two reasons for this. First of all, many coordinate changes and other transformations from well-known dynamical systems techniques do not respect the underlying network structure. Second of all, despite this somewhat ethereal' character, systems with a network structure often display behavior that is highly anomalous for general dynamical systems. Examples of this include very unusual bifurcation scenarios and high spectral degeneracies. As a possible explanation of this, it can be shown that a large class of network ODEs admit hidden symmetry, which may be discovered through the so-called fundamental network construction. In most cases, this underlying symmetry does not come from a group though, but rather from a more general algebraic structure such as a monoid or category. I will show how the fundamental network allows one to adapt techniques from dynamical systems theory to a network setting, and how some of the more unusual properties of networks may be explained. In doing so, I will mostly focus on spectral properties of linear network maps.

Tue Nov 27

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Nov 27

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Nov 27

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Nov 26

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Cuspforms with Compact Support [sic]
Paul Garrett, University of Minnesota
Mon Nov 26

## Applied and Computational Math Colloquium

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

Mon Nov 26

## Special Events and Seminars

3:35pm - Vincent Hall 207
Inverse transport theory and related applications
Ru-Yu Lai, University of Minnesota
##### Abstract:

The inverse transport problem consists of reconstructing the optical properties of a medium from boundary measurements. It finds applications in a variety of fields. In particular, radiative transfer equation (a linear transport equation) models the photon propagation in a medium in optical tomography. In this talk I will address results on the determination of these optical parameters. Moreover, the connection between the inverse transport problem and the Calderon problem will also be presented.

Mon Nov 26

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Cohomology of arithmetic groups and characteristic classes of manifold bundles
Bena Tshishiku, Harvard University
##### Abstract:

A basic problem in the study of fiber bundles is to compute the ring H*(BDiff(M)) of characteristic classes of bundles with fiber a smooth manifold M. When M is a surface, this problem has ties to algebraic topology, geometric group theory, and algebraic geometry. We have a good understanding of the cohomology in the "stable range", but this accounts for a small percentage of the total cohomology, and little is known beyond that. In this talk I describe some new characteristic classes (in the case dim M >>0) that come from the unstable cohomology of arithmetic groups.

Mon Nov 26

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Nov 26

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Solving PDEs with Deep Learning
Lexing Ying, Stanford University
##### Abstract:

In this talk, I will discuss some recent work on using deep neutral networks in solving high dimensional PDE problems. Examples include molecular dynamics, density functional theory, and inverse scattering problems. In each case, we propose novel neural network architectures based on the physical properties and sparse structures of the problem under investigation.

Mon Nov 26

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 23

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Nov 23

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar

Fri Nov 23

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Nov 23

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Nov 23

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 23

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Nov 23

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Nov 23

8:30am -
CANCELLED

Thu Nov 22

## Student Combinatorics Seminar

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

Thu Nov 22

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 22

## Differential Geometry and Symplectic Topology Seminar

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

Thu Nov 22

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Nov 22

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA
Thu Nov 22

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 22

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Nov 21

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Nov 20

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Nov 20

## Math Physics Seminar

12:20pm - Vincent Hall 313
Application of Invariant Signatures: Solving Jigsaw Puzzles
Rob Thompson

TBA

Tue Nov 20

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Nov 20

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Nov 19

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Semigroups and automorphic forms
Amy DeCelles, University of St. Thomas
Mon Nov 19

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Divide and conquer algorithms and software for large Hermitian eigenvalue problems
Yousef Saad, Department of Computer Science and Engineering, University of Minnesota
##### Abstract:

The solution of large symmetric real (or Hermitian complex) eigenvalue
problems is central to applications ranging from electronic structure
calculations to the study of vibrations in mechanical systems. A few
of these applications require the computation of a large number of
eigenvalues and associated eigenvectors. For example, when dealing
with excited states in quantum mechanics, it is not uncommon to seek a
few tens of thousands of eigenvalues of matrices of sizes in the tens
of millions. In such situations it is imperative to resort to
spectrum slicing' strategies, i.e., strategies that extract slices of
the spectrum independently. The presentation will discuss a few of
these techniques that are based on a combination of filtering
(polynomial, rational) and standard projection methods (Lanczos,
subspace iteration). The talk will also discuss our recently released
code named EVSL (for eigenvalues slicing library) that implements
these ideas.

Mon Nov 19

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: The spectrum of units of a height 2 theory
Jeremy Hahn, Harvard University
##### Abstract:

The space BSU admits two infinite loop space structures, one arising from addition of vector bundles and the other from tensor product. A surprising fact, due to Adams and Priddy, is that these two infinite loop spaces become equivalent after p-completion. I will explain how the Adams-Priddy theorem allows for an identification of sl_1(ku_p), the spectrum of units of p-complete complex K-theory. I will then describe work, joint with Andrew Senger, that attempts to similarly understand the spectrum of units of the 2-completion of tmf_1(3).

Mon Nov 19

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Nov 19

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lipschitz Regularized Deep Neural Networks Converge and are Robust to Adversarial Perturbations
##### Abstract:

Deep Neural Networks perform well in practice, but unlike traditional Machine Learning methods, they lack performance guarantees. This limits the use of the technology in real world and real time applications. The first step towards these guarantees is a proof of generalization. We will prove that Lipschitz regularized DNNs converge, and provide a rate of convergence, a stronger result which implies generalization. The regularization is related to the classical Lipschitz extension problem, and to inverse problems in Image Processing. It can be implemented in practice, and leads to robust networks which are more resistant to adversarial examples.

Joint work with Jeff Calder, available at https://arxiv.org/abs/1808.09540

Adam Oberman in a professor at McGill University. He studied at University of Toronto (Bachelors) and University of Chicago (PhD) before a postdoc at University of Texas, Austin, and a faculty position at Simon Fraser University. His research is on numerical methods for Partial Differential Equations, and more recently on optimization and Machine Learning.

Mon Nov 19

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 16

## MCFAM Seminar

5:30pm - Vincent Hall 16
No MCFAM Seminar

Fri Nov 16

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Cyclic Sieving, Necklaces, and Bracelets
Eric Stucky, University of Minnesota
##### Abstract:

One of the many interpretations of Catalan numbers is that Cn counts necklaces with n white beads and n+1 black beads. Motivated by this, we generalize the Catalan numbers and their q-analogues to many other necklaces. In this talk, we will discuss two surprising properties of these generalizations. First, they exhibit a q=-1 phenomenon with respect to necklace reflection, which can be extended to a cyclic sieving phenomenon for more exotic symmetries. Second, they conjecturally satisfy a "parity-unimodality" property, which in classical cases is a combinatorial shadow of a certain sl2 representation.

Fri Nov 16

## Probability Seminar

2:30pm - Vincent Hall 209
Macroscopic fluctuations through Schur generating functions
##### Abstract:

I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.

Fri Nov 16

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Nov 16

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 16

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Advanced Dynamics Systems Analysis and Synthesis for Future Storage Challenges
Raye Sosseh, Seagate Technology
##### Abstract:

Seagate is the global leader in data storage solutions, developing amazing products that enable people and businesses around the world to create, share and preserve their most critical memories and business data. Over the years the amount of information stored has grown from megabytes all the way to geopbytes, confirming the need to successfully store and access huge amounts of data. As demand for storage technology grows the need for greater efficiency and more advanced capabilities continues to evolve. Today data storage is more than just archiving; its about providing ways to analyze information, understand patterns and behavior, to re-live experiences and memories. Its about harnessing stored information for growth and innovation. Seagate is building on its heritage of storage leadership to solve the challenge of getting more out of the living information thats produced everyday. What began with one storage innovation has morphed into many systems and solutions becoming faster, more reliable and expansive. These considerations will be explored in this lecture on the application of Advanced Dynamics System Analysis & Synthesis to provide Solutions for future Storage Challenges.

Bio
Dr. Raye A. Sosseh is a managing Principal engineer and leads the Advanced Dynamics Group in Seagates Advanced Product Development department. His background is in dynamics and controls of embedded systems with particular applications to Hard Disk Drives. Dr. Sosseh holds a Ph.D. in Mechanical Engineering and a Masters in Electrical Engineering from the Georgia Institute of Technology. He joined Seagate in 2001 and has contributed to the staging and development of numerous products in Seagates Mission Critical and Cloud solutions swimlanes. Dr. Sosseh has over 10 patents assigned and pending patents. Raye and his family enjoy the lakes and restaurants in the Minneapolis area.

Fri Nov 16

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Partition algebras and their action on tensor space - continuation
Weiyan Chen, University of Minnesota
##### Abstract:

We continue with section 2.1 of the paper, On blocks of Delignes category Rep(S_t), by Comes and Ostrik. The longer term goal is to describe Deligne's category. In section 2.1 the partition algebras are introduced. They arose in work of Martin in a context of statistical mechanics, and were later shown by Jones to be in Schur-Weyl duality with the group algebras of symmetric groups. The exposition is introductory.

Fri Nov 16

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Nov 16

8:30am -
CANCELLED

Thu Nov 15

## Student Combinatorics Seminar

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

Thu Nov 15

## Colloquium

3:35pm - Vincent Hall 16
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems
Luca Spolaor, MIT
##### Abstract:

In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents. Finally I will describe some future applications of this method both in regularity theory and in other settings.

Thu Nov 15

## Differential Geometry and Symplectic Topology Seminar

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

Thu Nov 15

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Nov 15

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Physics of the Riemann-zeta function II
##### Abstract:

We continue to discuss how the Riemann-zeta function plays a role in different areas of physics, from condensed matter theory to quantum mechanics

Thu Nov 15

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 15

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Nov 14

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Nov 13

## Dynamical Systems

2:30pm - Ford Hall 130
Zigzagging of stripe patterns in growing domains
Montie Avery, University of Minnesota
##### Abstract:

The Swift-Hohenberg equation is a PDE which models formation of stripe and spot patterns in many physical settings. I will study a modification in which pattern formation is triggered by a propagating interface, and discuss the bifurcation structure based on the interface speed. I will focus on analytical results in reduced equations, in particular a singular perturbation problem for a system of ODEs arising from a traveling wave ansatz. I will also present numerical results in the Swift-Hohenberg and reduced equations which organize the bifurcation structure into a two-dimensional surface we call the moduli space. This is joint work with Ryah Goh, Oscar Goodloe, Alex Milewski, and Arnd Scheel.

Tue Nov 13

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Nov 13

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Nov 13

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Nov 12

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Semigroups and uniqueness of solutions of differential equations in automorphic forms
Amy DeCelles, University of St. Thomas
Mon Nov 12

## Applied and Computational Math Colloquium

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

Mon Nov 12

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Localizing the E_2 page of the Adams spectral sequence
Eva Belmont, Northwestern
##### Abstract:

The Adams spectral sequence is one of the central tools for calculating the stable homotopy groups of spheres, one of the motivating problems in stable homotopy theory. In this talk, I will discuss an approach for computing the Adams E_2 page for the sphere at p = 3 in an infinite region, by computing its localization by the non-nilpotent element b_{10}. This approach relies on computing an analogue of the Adams spectral sequence in Palmieri's stable category of comodules, which can be regarded as an algebraic analogue of stable homotopy theory. This computation fits in the framework of chromatic homotopy theory in the stable category of comodules.

Mon Nov 12

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Nov 12

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Rebecca Willett, University of Chicago
Mon Nov 12

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 09

## MCFAM Seminar

5:30pm - Vincent Hall 16
Macroecomic Analysis and Insight - Steepness of the Yield Curve As of September 2018
Ujae Kang, UnitedHealth Group
##### Abstract:

Ujae Kang will present on the Federal Reserve over the years and its influence on the yield curve. Then, he will cover what to expect from the Federal Reserve in the coming years.

Bio: Ujae Kang is Director of Enterprise Risk Management at UnitedHealth Group. He is an Associate of the Society of Actuaries and has an Master of Financial Mathematics from the University of Minnesota's School of Mathematics. He also provides economic research and insights to UnitedHealth Group's Asset Liability Management Committee as well as to other investors. For more information on Ujae go to linkedin.com/in/ujaeaugustinekang

Fri Nov 09

## Lie Theory Seminar

3:35pm - Vincent Hall 313
Motivic cohomology of Shimura varieties and level raising
Rong Zhou, Institute for Advanced Study
##### Abstract:

For a finite type scheme over a field, its motivic cohomology groups were defined by Voevodsky and are an important algebraic invariant. However, the properties of these groups are not well understood, and it is a difficult problem to exhibit explicit classes in motivic cohomology. We will construct such classes in the special fiber of Hilbert modular varieties by using the geometry of the supersingular locus. The construction is related to a geometric realization of the Jacquet-Langlands correspondence, as well as to level raising for Hilbert modular forms. A key ingredient is a form of Ihara's Lemma for compact quaternionic Shimura surfaces.

Fri Nov 09

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar

Fri Nov 09

## Probability Seminar

2:30pm - Vincent Hall 209
Low-temperature localization of directed polymers
Erik Bates, Stanford University
##### Abstract:

On the d-dimensional integer lattice, directed polymers are paths of a random walk that have been reweighted according to a random environment that refreshes at each time step. The qualitative behavior of the system is governed by a temperature parameter; if this parameter is small, the environment has little effect, meaning all possible paths are close to equally likely. If the parameter is made large, however, the system undergoes a phase transition at which the paths endpoint starts to localize. To understand the extent of this localization, we exploit the underlying Markov structure of the quenched endpoint distribution. The key difficulty is that the space of measures is too large for one to expect convergence results. By adapting methods appearing in the work of Mukherjee and Varadhan, we develop a compactification theory to resolve the issue. In this talk, we will discuss this intriguing abstraction, as well as new concrete theorems it allows us to prove for directed polymers constructed from SRW or any other walk. (joint work with Sourav Chatterjee)

Fri Nov 09

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 09

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Partition algebras and their action on tensor space
Weiyan Chen, University of Minnesota
##### Abstract:

We follow section 2.1 of the paper, On blocks of Delignes category Rep(S_t), by Comes and Ostrik. The longer term goal is to describe Deligne's category. In section 2.1 the partition algebras are introduced. They arose in work of Martin in a context of statistical mechanics, and were later shown by Jones to be in Schur-Weyl duality with the group algebras of symmetric groups. We introduce this theory.

Fri Nov 09

## MathCEP Seminar

10:10am - Vincent Hall 364
The Distributed Open Education Network (Doenet) and your dream educational technology
Duane Nykamp, University of Minnesota
##### Abstract:

A group of us are developing educational technology as part of the
Distributed Open Education Network (Doenet). We'll describe our vision for
an open educational technology ecosystem and highlight some solutions that
we are currently implementing. Then, we'll open the floor to discuss your
dreams for technological innovations that will enable you to better help
students learn.

Fri Nov 09

8:30am -
CANCELLED

Thu Nov 08

## Student Combinatorics Seminar

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

Thu Nov 08

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 08

## Differential Geometry and Symplectic Topology Seminar

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

Thu Nov 08

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Nov 08

## Special Events and Seminars

1:25pm - Vincent Hall 313
Irreducible components of affine Deligne--Lusztig varieties and orbital integrals
Rong Zhou, Institute for Advanced Study
##### Abstract:

Affine Deligne--Lusztig varieties (ADLV) naturally arise in the study of Shimura varieties and Rapoport--Zink spaces. Their irreducible components provide an interesting class of cycles on the special fiber of Shimura varieties. We prove a conjecture of Miaofen Chen and Xinwen Zhu, which relates the number of irreducible components of ADLV's to a certain weight multiplicity for a representation of the Langlands dual group. Our approach is to count the number of F_q points as q goes to infinity; this boils down to computing a certain twisted orbital integral. After applying techniques from local harmonic analysis, we reduce to computing a particular coefficient of the matrix for the inverse Satake transform. Using an interpretation of this coefficient in terms of a q-analogue of Kostant's partition function, we are able to reduce the problem to the previously known special cases of the conjecture proved by Hamacher--Viehmann and Nie. This is joint work with Yihang Zhu.

Thu Nov 08

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Physics of the Riemann-zeta function
##### Abstract:

I will give an overview of how the Riemann-zeta function plays a role in different areas of physics, from condensed matter theory to quantum mechanics.

Thu Nov 08

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 08

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Nov 07

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Nov 06

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Nov 06

## Math Physics Seminar

12:20pm - Vincent Hall 313
Contact Point Forces Acting on a Ball, Rolling on a Horizontal Plane and Actuated by Internal Point Masses
Stuart Rogers
##### Abstract:

This talk derives the contact point forces, namely the normal force and static friction, that act on a ball rolling without slipping on a horizontal plane. It is assumed that the ball is actuated by n point masses, which are free to move inside the ball. The dynamics of a disk and ball actuated by internal point masses are simulated numerically and the minimum coefficients of static friction required to prevent slippage are computed

Tue Nov 06

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Nov 06

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Nov 05

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Semigroups and uniqueness argument for solutions of differential equations in automorphic forms
Amy DeCelles, St. Thomas University
Mon Nov 05

## Applied and Computational Math Colloquium

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

Mon Nov 05

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: An isovariant Elmendorf's theorem
Sarah Yeakel, University of Maryland
##### Abstract:

An isovariant map is an equivariant map which preserves isotropy groups. Isovariant maps show up in equivariant surgery theory and in other settings when homotopy theory is applied to geometry. For a finite group G, we consider the category of G-spaces with morphisms given by isovariant maps. We will discuss a cofibrantly generated model structure on this category, along with isovariant versions of Elmendorf's theorem and a theorem of Klein and Williams about homotoping a map off a submanifold.

Mon Nov 05

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Nov 05

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Matthew Jacobs, University of California, Los Angeles
Mon Nov 05

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 02

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Nov 02

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Enumerating factorizations in GL_n(F_q)
Graham Gordon, University of Washington
##### Abstract:

Recently, many people, including Huang, Lewis, Morales, Reiner, and Stanton, have enumerated certain factorizations in GLnFq. Much of their results are essentially q-analogues of factorization enumerations coming from Sn in the q-->1 sense. I think this work constitutes a few significant puzzle pieces in an enormous, really difficult puzzle. I will talk about another piece (or fraction of a piece) of this puzzle that I can contribute, which is an enumeration of factorizations of the identity into a product of regular-elliptic elements. Ideally, this is q-analogous to a result of Stanley from the 1981, which enumerates factorizations of the identity into a product of n-cycles. Time permitting, I will talk about my approach and/or the geometry that corresponds to this work.

Fri Nov 02

## Probability Seminar

2:30pm - Vincent Hall 209
Dynamical freezing in a spin glass system with logarithmic correlations
Julian Gold, Northwestern University
##### Abstract:

We consider a continuous time random walk on the two-dimensional discrete torus, whose motion is governed by the discrete Gaussian free field on the corresponding box acting as a potential. More precisely, at any vertex the walk waits an exponentially distributed time with mean given by the exponential of the field and then jumps to one of its neighbors, chosen uniformly at random. We prove that throughout the low-temperature regime and at in-equilibrium timescales, the process admits a scaling limit as a spatial K-process driven by a random trapping landscape, which is explicitly related to the limiting extremal process of the field. Alternatively, the limiting process is a supercritical Liouville Brownian motion with respect to the continuum Gaussian free field on the box. Joint work with Aser Cortines (University of Zurich) and Oren Louidor (Technion).

Fri Nov 02

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Nov 02

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 02

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 409
Lecture
Joao Montero, Medtronic
Fri Nov 02

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Topology and combinatorics of the complex of injective words - continuation
Victor Reiner, University of Minnesota
##### Abstract:

I will continue the elementary treatment of properties of this complex, indicating situations where it arises, including a context considered by myself and Peter Webb.

Fri Nov 02

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Nov 02

9:30am -
CANCELLED

Thu Nov 01

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
My favorite facts about $\mathrm{GL}_n \mathbb{F}_q$
Graham Gordon, University of Washington
##### Abstract:

Have you ever heard that the symmetric group $\mathfrak{S}_n$ is equal to the finite general linear group $\mathrm{GL}_n \mathbb{F}_q$ in the limit $q \to 1$? This equality casts many mathematical shadows. I will discuss some of my favorites, which involve the (complex) characters of the two groups. I will include a primer on $\mathrm{GL}_n \mathbb{F}_q$ characters, and I will assume some foundational representation theory facts. Next, I will turn the tides and consider the limit $q \to \infty$. Mysteriously, some relationship between $\mathrm{GL}_n \mathbb{F}_q$ and $\mathfrak{S}_n$ as $q \to \infty$ is also casting shadows. Time permitting, I will discuss how character theory can be used to enumerate factorizations in order to segue into tomorrows seminar.

Thu Nov 01

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 01

## Differential Geometry and Symplectic Topology Seminar

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

Thu Nov 01

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Nov 01

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
The Stone-von Neumann Theorem
Joe Dickinson, University of Minnesota
##### Abstract:

I plan to talk about some number theoretic implications of the Stone-von Neumann theorem. The Stone-von Neumann theorem is a uniqueness theorem about commutation relations between position and momentum operators. I will give a historical discussion about number theory results implied by Stone-von Neumann.

Thu Nov 01

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 01

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Oct 31

## PDE Seminar

3:30pm - Vincent Hall 570
On the global regularity for Einstein-Klein-Gordon coupled system
Alexandru Ionescu, Princeton University
##### Abstract:

I will discuss the Einstein-Klein-Gordon coupled system of General
Relativity, and the problem of global stability of the Minkowski space-time.
This is joint work with Benoit Pausader.

Tue Oct 30

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Oct 30

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Oct 30

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Oct 30

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Oct 29

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Semigroups and uniqueness arguments for solutions of differential equations in automorphic forms
Amy DeCelles, St. Thomas University
Mon Oct 29

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Preconditioning systems of PDEs: from robust estimates to fast iterations, with applications to simulations of the brain
Ragnar Winther, University of Oslo
##### Abstract:

We will present a set up for simulations of the so-called glymphatic system, which is believed to
be an important mechanism for clearance of waste from the brain. Accumulation of waste can be coupled to
brain shrinkage and conditions like Alzheimers disease. An approach to design mathematical models for the
glymphatic system is to consider the brain as a poroelastic material, with complex geometry, bathed in water, and where various parameters of the model will vary over extreme ranges. A challenge in discretizing such systems in to design methods which behave well with respect variations of the parameters. In particular, we will explain how parameter robust stability estimates for the PDE systems can be used as a key tool to design effective algorithms for the corresponding discrete systems.

Mon Oct 29

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Symmetric monoidal categories and \Gamma-categories
Amit Sharma, Kent State University
##### Abstract:

A \Gamma-category is a functor from the category of finite based sets and basepoint preserving functions \Gamma^op to Cat. We construct a model category structure on the category of \Gamma-categories, which is symmetric monoidal closed to the Day convolution product. The fibrant objects in this model category structure are those
\Gamma-categories which are often called special \Gamma-categories. The main objective of this research is to establish a Quillen equivalence between a natural model category structure on the category of (small) permutative categories and strict symmetric monoidal functors Perm and our model category structure on \GammaCat. The weak equivalences of the natural model category structure are equivalences of underlying categories. In the paper [1], Segal defined a functor from the category of (small) symmetric monoidal categories into \GammaCat which can be described as a nerve functor for symmetric monoidal categories. The right adjoint \bar{K} of our Quillen equivalence is a thickening of Segal's nerve functor. We construct a permutative category L called Leinster's category, having the universal property that each \Gamma-category extends uniquely to a symmetric monoidal functor along an inclusion functor \Gamma^op > L. The left adjoint L of our Quillen equivalence is a composite functor composed of the symmetric monoidal extension functor indicated above followed by a homtopy colimit functor. In the paper [2], Mandell had shown that Segal's nerve functor (followed by the ordinary nerve functor) induces an equivalence between a homotopy category of Perm, obtained by inverting those strict symmetric monoidal functors which induce a weak homotopy equivalence of simplicial sets upon applying the nerve functor, and a homotopy category of \Gamma-spaces \GammaS obtained by inverting pre-stable equivalences which are those maps of \Gamma-categories which induce a degreewise weak homotopy equivalence of simplicial sets upon applying an E_\infty-completion functor. The objective of Mandell's work is to understand the relation between connective spectra and \Gamma-spaces obtained by applying the Segal's nerve functor to symmetric monoidal categories whereas our objective is to construct a model category of symmetric monoidal categories which is
symmetric monoidal closed.

References:
[1] G. Segal, Categories and cohomology theories, Topology 13 (1974) 293-312.
[2] M. A. Mandell, An Inverse K-theory functor, Doc. Math 15 (2010) 765-791.

Mon Oct 29

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Oct 29

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Pratik Chaudhari, University of California, Los Angeles
Mon Oct 29

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Oct 26

## MCFAM Seminar

5:30pm - Vincent Hall 16
Dynamic Linear Models
Katy Micek, 3M Finance
##### Abstract:

Dynamic linear models (DLMs), a subset of state space models, describe the output of a dynamic system as a function of a non-observable state process affected by random errors. Because DLMs can be used either for traditional time series analysis tasks (making inferences on observed states or prediction future observations) or for feature generation in machine learning tasks, they are a very useful tool for any data scientist who works with time series data. As a data scientist on the Data Analytics team for 3M Finance, I work primarily with time series data from the general ledger. Our team both leads data science projects and assists in organizational development of internal capabilities around data science.
In this talk, I will first provide an overview of the Finance organization and describe the technical tasks our team addresses. Next, I will give an introduction on the mathematics of DLMs. Finally, I will conclude showing examples of how DLMs can be used on time series data in a Jupyter notebook demo.

Fri Oct 26

## Algebraic Geometry

3:35pm - Vincent Hall 313
On rigid varieties with projective reduction
Shizhang Li, Columbia University
##### Abstract:

Bosch, Lütkebohmert and Raynaud laid down the foundation relating formal and rigid geometry. The type of questions they treat are mostly concerned with going from the rigid side to formal side. In the past, I considered the opposite type of question, namely to what extent properties on the formal side inform us about rigid geometry. More precisely, we will see what geometric consequences one can deduce under the assumption that the rigid space has a projective reduction. In this talk, I shall first say some background of rigid geometry and Raynaud's theory of formal models along with some examples. Then I will state the main theorem and a corollary. If time permitted, I will say something about the proof.

Fri Oct 26

## Combinatorics Seminar

3:35pm - Vincent Hall 570
High acyclicity of p-subgroup complexes for the symmetric groups
Cihan Bahran, University of Minnesota
##### Abstract:

For any finite group G and a fixed prime p, the topology of the poset of nontrivial elementary abelian p-subgroups contains significant information about the representations of G in characteristic p. For the symmetric group, this poset and its homology remain rather mysterious. A reasonable conjecture is that as we consider larger symmetric groups, the associated posets should get topologically more connected. I will rephrase this conjecture as a representation stability phenomenon ala Church-Ellenberg-Farb, and provide evidence for it by exhibiting high acyclicity of certain subposets.t:

Fri Oct 26

## Probability Seminar

2:30pm - Vincent Hall 209
Some Problems of Robust High-dimensional Statistics
##### Abstract:

The talk will first review the problem of robust subspace recovery, which seeks an underlying low-dimensional subspace in a data set that is possibly corrupted with outliers. The emphasis will be on surveying existing theoretical guarantees and tradeoffs. New results for adversarial outliers will also be mentioned. Following this, other related problems will be discussed, along with new results for one of these problems.

Fri Oct 26

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Oct 26

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Oct 26

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Topology and combinatorics of the complex of injective words
Victor Reiner, University of Minnesota
##### Abstract:

According to a result of Farmer, the homology of this complex vanishes except in the bottom and top dimensions. This property is a consequence of shellability of the complex. We will discuss these matters, used in a proof of Nakaoka's theorem on stability of the corestriction map in the group homology of the symmetric groups.

Fri Oct 26

## MathCEP Seminar

10:10am - Vincent Hall 364
The Chicago Guide to Writing about Numbers Book Discussion
Journal Club
##### Abstract:

People who work well with numbers are often stymied by how to write about them. Those who don't often work with numbers have an even tougher time trying to put them into words. For instance, scientists and policy analysts learn to calculate and interpret numbers, but not how to explain them to a general audience. Students learn about gathering data and using statistical techniques, but not how to write about their results. And readers struggling to make sense of numerical information are often left confused by poor explanations. Jane Miller, an experienced research methods and statistics teacher, gives writers the assistance they need. The Chicago Guide to Writing about Numbers helps bridge the gap between good quantitative analysis and good expository writing. Field-tested with students and professionals alike, this book shows writers how to think about numbers during the writing process. By providing basic guidelines for successfully using numbers in prose, The Chicago Guide to Writing about Numbers will help writers of all kinds clearly and effectively tell a story with numbers as evidence.

Fri Oct 26

9:30am -
CANCELLED

Thu Oct 25

## Student Combinatorics Seminar

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

Thu Oct 25

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 25

## Algebraic Geometry

1:25pm - Vincent Hall 313
An example of liftings with different Hodge numbers
Shizhang Li, Columbia University
##### Abstract:

Does a smooth proper variety in positive characteristic know the Hodge numbers of its liftings? The answer is "of course not". However, it's not that easy to come up with a counter-example. In this talk, I will first introduce the background of this problem. Then I shall discuss some obvious constraints of constructing a counter-example. Lastly I will present such a counter-example and state a few questions of similar flavor for which I do not know an answer.

Thu Oct 25

## Differential Geometry and Symplectic Topology Seminar

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

Thu Oct 25

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Oct 25

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Cryptographic Multilinear Maps from Elliptic Curves
Mahrud Sayrafi, University of Minnesota
##### Abstract:

We will begin with defining cryptographic multilinear maps, briefly discussing some of their applications, and referencing one such map from Boneh-Silverberg '03. After that, we will extend a problem involving isogenies of elliptic curves into an open problem of finding cryptographic invariant maps from Boneh, et al. '18.stract:

Thu Oct 25

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Oct 25

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Oct 24

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Oct 23

## Dynamical Systems

2:30pm - Ford Hall 130
Snaking in the Swift-Hohenberg Equation in Dimension 1+Epsilon
Jason Bramburger, Brown University
##### Abstract:

The Swift-Hohenberg equation is a widely studied partial differential equation which is known to support a variety of spatially localized structures. The one-dimensional equation exhibits spatially localized steady-state solutions which give way to a bifurcation structure known as snaking. That is, these solutions bounce between two different values of the bifurcation parameter while ascending in norm. The mechanism that drives snaking in one spatial dimension is now well-understood, but recent numerical investigations indicate that upon moving to two spatial dimensions, the related radially-symmetric spatially-localized solutions take on a significantly different snaking structure which consists of three major components. To understand this transition we apply a dimensional perturbation in an effort to use well-developed methods of perturbation theory and dynamical systems. In particular, we are able to identify key characteristics that lead to the segmentation of the snaking branch and therefore provide insight into how the bifurcation structure changes with the spatial dimension.

Tue Oct 23

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Oct 23

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Oct 23

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Oct 22

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Hamiltonians
##### Abstract:

We apply methods of quantum mechanics to construct self-adjoint, purely discrete pseudo-differential operators which characterize a nuclear Frechet Schwartz space of automorphic forms.

Mon Oct 22

## Applied and Computational Math Colloquium

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

Mon Oct 22

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Finitely generated sequences of linear subspace arrangements
##### Abstract:

Hyperplane arrangements are a classical meeting point of topology, combinatorics and representation theory. Generalizing to arrangements of linear subspaces of arbitrary codimension, the theory becomes much more complicated. However, a crucial observation is that many natural sequences of arrangements seem to be defined using a finite amount of data.

In this talk I will describe a notion of 'finitely generation' for collections of arrangements, unifying the treatment of known examples. Such collections turn out to exhibit strong forms of stability, both in their combinatorics and in their cohomology representation. This structure makes the appearance of representation stability transparent and opens the door to generalizations.

Mon Oct 22

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Oct 22

## IMA Data Science Lab Seminar

1:25pm - Lind 409
Large Sample Asymptotics of Graph-based Methods in Machine Learning: Mathematical Analysis and Implications
Nicolas Garcia-Trillos, University of Wisconsin, Madison
##### Abstract:

Many machine learning procedures aimed to extract information from data can be defined as precise mathematical objects that are constructed in terms of the data. It is often assumed that the data is big in complexity but also in quantity, and in this large amount of data setting, a basic mathematical concept that one can explore is that of closure of a given class of statistical procedures (i.e. what are the limiting procedures as the number of data points available goes to infinity.) In this talk, I will explore this notion in the context of graph-based methods. Examples of such methods include minimization of Cheeger cuts, spectral clustering, and graph-based bayesian semi-supervised learning, among others. I will introduce some of the mathematical ideas needed for the analysis, as well as show some of the implications of it: our results show statistical consistency of the methods, provide with quantitative information in the form of scaling of parameters and rates of convergence, imply qualitative properties at the discrete level, and suggest the use of appropriate algorithms.

Mon Oct 22

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Oct 19

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Oct 19

## Lie Theory Seminar

4:30pm - Vincent Hall 313
On Several Classical Number Theory Problems
Tianxin Cai, Zhejiang University and University of Iowa
Fri Oct 19

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Optimal switching sequence for switched linear systems
Qie He, UMN
##### Abstract:

We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n real matrices and an n-dimensional real vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the given vector. This simple problem has many applications in operations research and control, yet a moderate-sized instance is challenging to solve to optimality for state-of-the-art optimization software. We propose a simple exact algorithm for this problem. The efficiency of our algorithm depends heavily on whether the given set of matrices has the oligo-vertex property, a concept we introduce for a finite set of matrices. The oligo-vertex property captures how the numbers of extreme points for a sequence of K convex polytopes related to the given matrices grow with respect to K. We derive several sufficient conditions for a set of matrices to have this property, and pose several open questions related to this property.

Fri Oct 19

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Oct 19

## Differential Geometry and Symplectic Topology Seminar

2:30pm - Vincent Hall 6
The Smooth 4-dimensional Poincare Conjecture and Dehn surgery on links
##### Abstract:

The smooth version of the 4-dimensional Poincare Conjecture (S4PC) states that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere. One way to attack the S4PC is to examine a restricted class of 4-manifolds. For example, Gabai's proof of Property R implies that every homotopy 4-sphere built with one 2-handle and one 3-handle is standard. In this talk, we consider homotopy 4-spheres X built with two 2-handles and two 3-handles, which are uniquely determined by the attaching link L for the 2-handles in the 3-sphere. We prove that if one of the components of L is the connected sum of a torus knot T(p,2) and its mirror (a generalized square knot), then X is diffeomorphic to the standard 4-sphere. This is joint work with Jeffrey Meier.

Fri Oct 19

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Oct 19

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
A theorem of Nakaoka on the homology of symmetric groups - continuation
Peter Webb, University of Minnesota
##### Abstract:

A theorem of Nakaoka states that the inclusion of symmetric groups induces an isomorphism of group homology provided that the degrees of the symmetric groups are large enough. This week I will continue with the proof of this, explaining the equivariant cohomology spectral sequence and the specific calculations that arise, trying to assume as little as I can.

Fri Oct 19

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Oct 19

9:30am -
CANCELLED

Thu Oct 18

## Student Combinatorics Seminar

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

Thu Oct 18

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 18

## Differential Geometry and Symplectic Topology Seminar

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

Thu Oct 18

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Computations in Local Rings using Macaulay2
Mahrud Sayrafi, University of Minnesota
##### Abstract:

Local rings are ubiquitous in commutative algebra and algebraic geometry. In this talk I will describe two avenues for computing in local rings with respect to prime ideals, first using the associated graded algebra and then using only Nakayama's lemma. Time permitting, I will demonstrate various examples and applications, such as computing the Hilbert-Samuel multiplicity, using Macaulay2.

Thu Oct 18

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Elliptic functions and elliptic curves in the 19th century
##### Abstract:

We will give an account of the work on Weierstrass and Jacobi proving a result due to Abel on meromorphic functions on the torus. These are results about complex points of elliptic curves which suggest attributes for rational points. These examples were later greatly extended at the hands of several mathematicians and reached a high-point with the GAGA principle by Serre. It's also the first example of a Riemann-Roch type theorem which were greatly extended by Grothendieck, Atiyah and Singer. Only some familiarity with Cauchy's theorem in complex analysis is needed to understand the talk.

Thu Oct 18

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Oct 18

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Oct 17

## PDE Seminar

3:30pm - Vincent Hall 570
Continuum Limits of Semi-Supervised Learning on Graphs
Matthew Thorpe, University of Cambridge
##### Abstract:

Given a data set $\{x_i\}_{i=1}^n$ with labels $\{y_i\}_{i=1}^N$ on the first $N$ data points the goal of semi-supervised is to infer labels on the remaining $\{x_i\}_{i=N+1}^n$ data points. In this talk we use a random geometric graph model with connection radius $r(n)$. The framework is to consider objective functions which reward the regularity of the estimator function and impose or reward the agreement with the training data, more specifically we will consider discrete p-Laplacian and fractional Laplacian regularization.

The talk concerns the asymptotic behaviour in the limit where the number of unlabelled points increases while the number of training points remains fixed. The results are to uncover a delicate interplay between the regularizing nature of the functionals considered and the nonlocality inherent to the graph constructions. I will give almost optimal ranges on the scaling of $r(n)$ for asymptotic consistency to hold. Furthermore, I will setup the Bayesian interpretation of this problem.

This is joint work with Matt Dunlop (Caltech), Dejan Slepcev (CMU) and
Andrew Stuart (Caltech).

Mathew Thorpe is a Research Fellow at the Cantab Capital Institute for the Mathematics of Information, Department of Applied Mathematics and Theoretical Physics, University of Cambridge.

.

Tue Oct 16

## Dynamical Systems

2:30pm - Ford Hall 130
Run-and-tumble clusters: blowing up the blowup
Arnd Scheel
##### Abstract:

Motivated by patterns in colonies of myxobacteria, I will show some results on clustering in run-and-tumble processes. We look at two populations of agents on the real line, propagating with speed 1 to the left or to the right, respectively. They tumble, that is, reverse direction, with a rate that depends on encounters with agents traveling in the opposite direction in a nonlinear fashion. I will show some phenomena and then explain how elementary dynamical systems methods can help understanding the formation of localized clusters in the population. The talk should be accessible to graduate students with basic knowledge in dynamical systems

Tue Oct 16

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Oct 16

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Oct 16

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Oct 15

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Hamiltonians
##### Abstract:

We apply methods in quantum mechanics to construct self-adjoint, purely discrete pseudo-differential operators which characterize a nuclear Fréchet Schwartz space of automorphic forms"

Mon Oct 15

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Modeling gas, fluid, and particle transport in the lung airway system: the curse of scales
Marcel Filoche, Ecole Polytechnique, Paris
##### Abstract:

The pulmonary airway system is a highly hierarchical tree-like 3D network in charge of transferring oxygen from the upper airways down to the alveolar region where the gas exchange occurs between air and blood. It is also the place of numerous particle and fluid transport processes. Given the complexity of the anatomy and of the physics involved, numerical simulation is a remarkable tool for investigating the properties of this organ seen as a "transport system", understanding its behavior and possible failures, and predicting the outcome of therapies. However, the range of scales represents here a huge challenge: from the meter scale of the entire organ size down to the micron scale of the mucus layer, about 5 to 6 orders of magnitude of length scale are crossed.

In this talk, we will present several examples of numerical models able to capture the various aspects of the lung airway system, from the simplest linear approach of gas transport to more advanced computational fluid dynamics simulation. We will show, in particular, how the range of scales involved and the difficulty to access the actual parameters in the patient imposes to use a hierarchy of models and a diversity of numerical techniques. We will explain how these models can be used either to reach a general understanding of the system or to design patient specific diagnosis and therapy.

Mon Oct 15

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Rigidity of warped cones and coarse geometry of expanders
Wouter van Limbeek, UIC
##### Abstract:

Finitely generated subgroups of compact Lie groups give rise to expander graphs via a warped cone construction. We study the dependence of the coarse geometry of such expander graphs on the original subgroup and establish a dynamical analogue of quasi-isometric rigidity theorems in geometric group theory: Namely, the coarse geometry of the warped cone determines the subgroup up to commensurability, unless the group has abelian factors. This is joint work with David Fisher and Thang Nguyen.

Mon Oct 15

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Oct 15

## IMA Data Science Lab Seminar

1:25pm - Keller 3-180
Lecture
Mon Oct 15

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Oct 12

## MCFAM Seminar

5:30pm - Vincent Hall 16
Interpreting Constraints in Mean Variance Optimization
Chris Bemis, Head of Quantitative Analysis and Research, Whitebox Advisors, UMN Math Dpt. Affiliated Faculty
##### Abstract:

We study the effect linear constraints have on risk in the context of mean variance optimization (MVO). Jagannathan and Ma (2003) establish an equivalence between certain constrained and unconstrained MVO problems via a modification of the covariance matrix. We extend their results to arbitrary linear constraints and provide alternative interpretations for the effect of constraints on both the input parameters to the problems at hand and why ex-post performance is improved in the constrained setting.

Fri Oct 12

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Basis shape loci and the positive Grassmannian
Cameron Marcott, University of Waterloo
##### Abstract:

We study the set of k-dimensional planes in Rn admitting a basis of vectors with prescribed supports. We describe conditions on the prescribed support shape for when this set of planes has the expected dimension in the Grassmannian, and for when this set of planes intersects the positive Grassmannian in its full dimension.

Fri Oct 12

## Probability Seminar

2:30pm - Vincent Hall 209
Brascamp-Lieb inequalities for even functions
Liran Rotem, UMN
##### Abstract:

It was observed by Cordero-Erausquin, Fradelizi and Maurey that the classical Gaussian Poincare Inequality can be improved by a factor of 2 if we restrict our attention to even functions. They used this improved inequality to answer a geometric question asked by Banaszczyk about convexity of the Gaussian measure.

The Gaussian Poincare inequality is a special case of a more general variance inequality due to Brascamp and Lieb. In general, it is not clear how to improve this more general inequality in the even case. Again, this question turns out to be closely related to certain geometric problems. In this talk we will prove a sharp even Brascamp-Lieb inequality for measures of the form exp(-|x|^p). To do so we will also present a new weighted Poincare inequality which holds for ODD functions.

Based on joint work with Dario Cordero-Erausquin.

Fri Oct 12

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Oct 12

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Oct 12

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Jennifer Schumacher, 3M
Fri Oct 12

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
A theorem of Nakaoka on the homology of symmetric groups
Peter Webb, University of Minnesota
##### Abstract:

A theorem of Nakaoka states that the inclusion of symmetric groups induces an inclusion of group homology provided that the degrees of the symmetric groups are large enough. A proof of this statement in homological stability can be given using the equivariant cohomology of the complex of injective words. I will start describing the machinery needed to give this proof, trying to assume as little as I can.

Fri Oct 12

## MathCEP Seminar

10:10am - Vincent Hall 364
Adventures with experiential and active learning
Rina Ashkenazi, University of Minnesota
##### Abstract:

I will share my attempts to include real world experiences and active learning in the actuarial mathematics curriculum. Those include a design of a project based course (MATH 4067W) that is instructed in collaboration with practicing actuaries, as well as the inclusion of small projects and in-class presentations in other, existing courses.

Fri Oct 12

9:30am -
CANCELLED

Thu Oct 11

## Student Combinatorics Seminar

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

Thu Oct 11

## Colloquium

3:35pm - Vincent Hall 16
Propagation of bistable fronts through a perforated wall
Hiroshi Matano, Meiji University, Tokyo, Ordway Visitor
##### Abstract:

We consider a bistable reaction-diffusion equation on ${\bf R}^N$ in the presence of an obstacle $K$, which is a wall of infinite span with periodically arrayed holes. More precisely, $K$ is a closed subset of ${\bf R}^N$ with smooth boundary such that its projection onto the $x_1$-axis is bounded, while it is periodic in the rest of variables $(x_2,\ldots, x_N)$. We assume that ${\bf R}^N \setminus K$ is connected. Our goal is to study what happens when a planar traveling front coming from $x_1 = +\infty$ meets the wall $K$.

We first show that there is clear dichotomy between propagation' and blocking'. In other words, the traveling front either completely penetrates through the wall or is totally blocked, and that there is no intermediate behavior. This dichotomy result will be proved by what we call a De Giorgi type lemma for an elliptic equation on ${\bf R}^N$. Then we will discuss sufficient conditions for blocking, and those for propagation. This is joint work with Henri Berestycki and Francois Hamel.

Thu Oct 11

## Differential Geometry and Symplectic Topology Seminar

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

Thu Oct 11

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Oct 11

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA
Thu Oct 11

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Oct 11

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Oct 10

## PDE Seminar

3:35pm - Vincent Hall 570
Soliton resolution for the critical nonlinear heat equation
Hiroshi Matano, Meiji University
##### Abstract:

In this talk, I will discuss the asymptotic behavior of radially symmetric solutions of the nonlinear heat equation on ${\bf R}^N$ $(N > 2)$ with the Sobolev critical power nonlinearity.

In the case of time-global solutions, we show that the solution is asymptotically decomposed into a finite sum of rescaled ground states that hardly interact with each other because the ratio of the rescaling parameters of different solitons tends to infinity. The total energy of the solution then converges to an integer multiple of the energy of the ground state. We call this behavior soliton resolution" of the solution.

In the case where the solution blows up in finite time, and if the blow-up is of type II in a certain sense, we show that a similar soliton resolution occurs near the blow-up point.

Finally we will show the existence of a multi-soliton time-global solution for the case $N > 6$. This is joint work with Frank Merle.

Tue Oct 09

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Oct 09

## Math Physics Seminar

12:20pm - Vincent Hall 313
Signal Processing and Classification
Jimmy Broomfield
##### Abstract:

This talk will center around signal classification and it will include a demonstration in python. We will focus on how exploring three major
feature domains: The original time sampled data, the frequency domain, and the use of wavelet decompositions. A range of real world applications
will be discussed

Tue Oct 09

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Oct 09

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Oct 08

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Two applications of differential equations to automorphic forms
Kim Klinger-Logan, University of Minnesota
Mon Oct 08

## Applied and Computational Math Colloquium

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

Mon Oct 08

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: A chromatic approach to tmf cooperations
Paul van Koughnett, Purdue
##### Abstract:

The topological modular forms spectrum, tmf, is a cohomology theory constructed from elliptic curves that captures information about stable homotopy at chromatic heights less than or equal to 2. We present a description of the height 1 part of the algebra of tmf cooperations, and interpret it in terms of modular forms. This is joint work with Dominic Culver.

Mon Oct 08

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Oct 08

## IMA Data Science Lab Seminar

1:25pm - Lind 305
A PDE Approach to a Prediction Problem Involving Randomized Strategies
Nadejda Drenska, University of Minnesota, Twin Cities
##### Abstract:

This work investigates a classical problem from online machine learning using methods from optimal control theory. The problem is a discrete time iterative process involving decision making at every step; the goal for mathematical analysis is to understand the optimal strategy and its consequences over a long period of time. The solution is analyzed through its continuous limit--an appropriately defined value function, which solves a PDE in the viscosity sense. The PDE is then used to determine the optimal strategies.

Bio
Nadejda went to Brown University as an undergraduate. She graduated with her Ph.D. in mathematics from the Courant Institute (NYU) with an adviser Robert Kohn. Nadejda is now a MCFAM postdoc at the University of Minnesota.

Mon Oct 08

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Oct 05

## MCFAM Seminar

5:30pm - Vincent Hall 16
CCAR (Comprehensive Capital Analysis and Review) and Basel Framework - Risk Management Modeling
Dr. Xu Li
##### Abstract:

Dr.Xu Li will give an overview of what he is does in Market Risk Analytics as a SVP of Risk Analytics at Citi. He will then focus on a default model that is useful for both CCAR, the stress testing framework set out by the Federal Reserve (IDR) and Basel framework which is the international regulatory framework for banks (IRC, DRC). He will show the general ideas on modeling the default risks and discuss some options on the modeling choices.

Fri Oct 05

## Combinatorics Seminar

3:35pm - Vincent Hall 570
The Rogers-Ramanujan identities- a historical view
Dennis Stanton, UMN
##### Abstract:

I will survey proofs of these identities, starting with Rogers in 1894. Included are excursions into q-series, partitions, combinatorics, Lie algebras, symmetric functions, statistical mechanics, probability and finite fields. I shall conclude with recent refinements in joint work with O'Hara.

Fri Oct 05

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Oct 05

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Oct 05

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Oct 05

9:30am -
CANCELLED

Thu Oct 04

## Student Combinatorics Seminar

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

Thu Oct 04

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 04

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Stability of Ricci solitons
Huaidong Cao - Ordway Visitor, Lehigh University
##### Abstract:

In this talk we continue our discussion of the previous week on stability of
Ricci solitons, especially in four dimensions.

Thu Oct 04

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Oct 04

## Special Events and Seminars

1:25pm - Vincent Hall 313
The Langlands-Kottwitz-Scholze method for Shimura varieties of abelian type
Alex Youcis, University of California, Berkeley
##### Abstract:

The local (and global) Langlands conjectures attempt to bridge the major areas of harmonic analysis and number theory by forming a correspondence between representations which naturally appear in both areas. A key insight due to Langlands and Kottwitz is that one could attempt to understand such a conjectural correspondence by comparing the traces of natural operators on both sides of the bridge. Moreover, it was realized that Shimura varieties present a natural means of doing this. For global applications, questions of reduction type (at a particular prime p) for these Shimura varieties can often be avoided, and for this reason the methods of Langlands and Kottwitz focused largely on the setting of good reduction. But, for local applications dealing with the case of bad reduction is key. The setting of bad reduction was first dealt with, for some simple Shimura varieties, by Harris and Taylor which they used, together with the work of many other mathematicians, to prove the local Langlands conjecture for GL_n. A decade later Scholze gave an alternative, more geometric, way to understand the case of bad reduction for certain Shimura varieties and was able to reprove the local Langlands conjecture for GL_n. In this talk we will discuss an extension of the ideas of Scholze to a wider class of Shimura varieties, as well as the intended application of these ideas to the local Langlands conjectures for more general groups.

Thu Oct 04

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory

Thu Oct 04

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Oct 04

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Oct 03

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Oct 02

## Ordway Lecture Series

2:30pm - Vincent Hall 16
Microlocal codimension-three conjecture
Kari Vilonen, University of Melbourne, Ordway Visitor
##### Abstract:

Special functions (or distributions) can be understood and analyzed in terms of the systems of differential equations they satisfy. To this end, a general theory of systems of linear (micro) differential equations was developed by the Sato school in Kyoto. This point of view, in its various incarnations, is now ubiquitous in many parts of mathematics. For example, in the geometric Langlands program and representation theory it allows us to replace functions and group representations by geometric objects, perverse sheaves or D-modules. It has been well-known for a long time that the description of these objects gains more symmetry when one passes to the cotangent bundle. We explain the shape of the general microlocal structure of these objects and discuss, in particular, the role played by the codimension-three conjecture which was proved by Masaki Kashiwara and the speaker a few years ago.

Tue Oct 02

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Oct 02

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Oct 02

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Oct 02

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Oct 01

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Lax-Phillips in rational-rank one
Paul Garrett
Mon Oct 01

## Applied and Computational Math Colloquium

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

Mon Oct 01

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Grothendieck-Teichmuller group and braided Hopf algebras
Craig Westerland, University of Minnesota
##### Abstract:

The primitives in a classical Hopf algebra form a Lie algebra (in fact, a Lie subalgebra of the Hopf algebra).  For a braided Hopf algebra, this is no longer the case.  Consequently, all of the structure theorems for Hopf algebras (e.g., the Milnor-Moore and Poincaré-Birkhoff-Witt theorems) break down in this setting. This is a report on ongoing work in which we construct an operad (a braided form of the Lie operad) which governs the algebraic structure of the primitives in a braided Hopf algebra.  We can interpret this operad in terms of the homology of covering spaces of the 2-dimensional little disks operad.  This gives rise to an action of Drinfeld's Grothendieck-Teichmuller group on this operad which may be related to Drinfeld's original definition of this group.

Mon Oct 01

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Oct 01

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Tyler Whitehouse, Gigantum
Mon Oct 01

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Sep 28

## MCFAM Seminar

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

Fri Sep 28

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Pattern inventory polynomials for consonances and dissonances
Octavio Agustín-Aquino, Universidad Tecnológica de la Mixteca
##### Abstract:

Dennis White obtained formulas from the Pólya-Redfield theory for counting patterns with a certain group of automorphisms. We apply this to the problem of counting the so-called strong dichotomies, which are self-complementary rigid patterns of equitempered scales with an even number of tones. Strong dichotomies are models for the selection of consonances and dissonances in counterpoint, and are of capital importance for Guerino Mazzola's counterpoint theory. Furthermore, pattern inventory polynomials for strong dichotomies exhibit, in certain cases, a kind of cyclic sieving phenomenon, and we conjecture that there is a nice regularity for the cases when this holds true.

Fri Sep 28

## Probability Seminar

2:30pm - Vincent Hall 209
Stationary coalescing walks on the lattice
Arjun Krishnan, University of Rochester
##### Abstract:

Consider a measurable dense family of semi-infinite nearest-neighbor paths on the integer lattice in d dimensions. If the measure on the paths is translation invariant, we completely classify their collective behavior in d=2 under mild assumptions. We use our theory to classify the behavior of semi-infinite geodesics in random translation invariant metrics on the lattice; it applies, in particular, to first- and last-passage percolation. We also construct several examples displaying unexpected behaviors. (joint work with Jon Chaika)

Fri Sep 28

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Sep 28

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Sep 28

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
If a tree falls in the woods and nobody hears, does it make a sound? (Or, making sure your code runs anywhere.)
Tyler Whitehouse, Gigantum
##### Abstract:

Most researchers dont have the time or the skill to apply the kinds of software development best practices needed to make their computational work transparent, reproducible, and easy to use. Despite repeated calls by publishers and funders to include usable and understandable code with publications, it is still too much work to be done with the resources allotted. Such problems are not unique to academia, and the penetration of machine learning and data science in industry has brought these issues to the attention of commercial enterprise as well. Reproducibility is a problem for everyone.

This talk will demonstrate an open source data science platform that automates the issues around transparency, reproducibility, and ease of use for work done in open source languages and frameworks like Python and R. It will show how easy it is to set up computational and data science environments of varying complexity that can be shared with anybody in the world with no extra labor or set up.

Bio
Tyler Whitehouse did an undergraduate degree in math at UC Santa Cruz and a Ph.D. at the University of Minnesota. He graduated in 2009 after working with Professor Gilad Lerman on problems dealing with the rectifiability of sets and measures in Hilbert spaces, then going on to Vanderbilt University as a postdoc for 3 years. From 2012 to 2017 he worked as a data scientist and consultant in the Washington DC area. Currently, he is the president of a data science software startup in the DC area.

Fri Sep 28

9:30am -
CANCELLED

Thu Sep 27

## Student Combinatorics Seminar

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

Thu Sep 27

## Analysis and PDE Working Seminar

3:40pm - Ford Hall 155
Mean Field Games
Sam Stewart
##### Abstract:

Finding emergent equilibria of games with finitely many players is hard, especially if players' strategies depend on each other. For example, what is the best strategy to escape a crowded room? Each player has to mentally simulate the potential strategies of other players so best strategies become recursive. Lasry and Lions (Pierre Lions is a Fields medalist for other work) devised a framework (mean field games) in 2007 for connecting these games to PDEs. The idea is simple: take the number of players to infinity and instead track a density and its velocity (strategy) field. Two coupled PDEs emerge, one in forward time (describing the world evolution) in one in backward time describing the best strategies. In this talk, I'll give a brief intro and then outline a cool example: crowd waves in soccer stadiums. A dead-simple mean field game model predicts traveling waves as long as the stadium's diameter isn't too small.

Thu Sep 27

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Speaker:
Affiliation:
Abstract

Thu Sep 27

## Ordway Lecture Series

3:35pm - Vincent Hall 16
Microlocal codimension-three conjecture
Kari Vilonen, University of Melbourne, Ordway Visitor
##### Abstract:

Special functions (or distributions) can be understood and analyzed in terms of the systems of differential equations they satisfy. To this end, a general theory of systems of linear (micro) differential equations was developed by the Sato school in Kyoto. This point of view, in its various incarnations, is now ubiquitous in many parts of mathematics. For example, in the geometric Langlands program and representation theory it allows us to replace functions and group representations by geometric objects, perverse sheaves or D-modules. It has been well-known for a long time that the description of these objects gains more symmetry when one passes to the cotangent bundle. We explain the shape of the general microlocal structure of these objects and discuss, in particular, the role played by the codimension-three conjecture which was proved by Masaki Kashiwara and the speaker a few years ago.

Thu Sep 27

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Second variation of Perelman's entropy and stability of Ricci solitons
Huaidong Cao, Ordway Visitor, Lehigh University
##### Abstract:

Einstein metrics are critical points of the well-known classical Hilbert action
(namely the total scalar curvature functional) under volume normalization. Likewise,
Ricci solitons are critical points of Perelman's entropy.
In this talk, we shall discuss the second variation of Perelman's entropy and stability
of compact Ricci solitons. It turns out the stability for positive Einstein manifolds is
related to two eigenvalue estimates: the first eigenvalue of the Laplacian on functions,
and that of the Lichnerowicz Laplacian on symmetric 2-tensors.

Thu Sep 27

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Sep 27

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory

Thu Sep 27

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Sep 27

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Sep 26

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Sep 25

## Colloquium

3:35pm - Vincent Hall 16
Microlocal codimension-three conjecture
Kari Vilonen, University of Melbourne, Ordway Visitor
##### Abstract:

Special functions (or distributions) can be understood and analyzed in terms of the systems of differential equations they satisfy. To this end, a general theory of systems of linear (micro) differential equations was developed by the Sato school in Kyoto. This point of view, in its various incarnations, is now ubiquitous in many parts of mathematics. For example, in the geometric Langlands program and representation theory it allows us to replace functions and group representations by geometric objects, perverse sheaves or D-modules. It has been well-known for a long time that the description of these objects gains more symmetry when one passes to the cotangent bundle. We explain the shape of the general microlocal structure of these objects and discuss, in particular, the role played by the codimension-three conjecture which was proved by Masaki Kashiwara and the speaker a few years ago.

Tue Sep 25

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Sep 25

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Sep 24

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Lax-Phillips estimates [cont'd]
Paul Garrett
Mon Sep 24

## Topology Seminar

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

Mon Sep 24

## Dynamical Systems

2:30pm - Vinent Hall 570
Water transport in models of dryland vegetation patterns
Punit Gandhi, MBI, Ohio-State University
##### Abstract:

Regular spatial patterns in the vegetation growth of dryland ecosystems are thought to arise through self-organization in response to water scarcity. This behavior has been qualitatively reproduced by reaction-advection-diffusion systems that model various interactions between the plants and their environment. The patterns most often appear on very gentle slopes as bands of vegetation separated by bare soil with characteristic spacing on the order of 100 meters. I will use a simple modeling framework and an idealized topography to discuss the role of water transport in determining (1) the shape of individual vegetation bands and (2) the region of the landscape occupied vegetation patterns. The results are in qualitative agreement with observations from remote sensing data, and suggest that the placement of the patterns relative to ridges and valleys on the terrain may provide some indication of resilience to ecosystem collapse under aridity stress. I will also discuss prospects for improved water transport models that provide a more detailed picture of processes governing surface/subsurface water dynamics across timescales.

Mon Sep 24

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Genetics of mRNA and Protein Expression in Large Yeast Populations
Frank Albert, University of Minnesota, Twin Cities
##### Abstract:

Genetic variation among individuals is an important source of phenotypic variation within species. Many of these genetic effects are due to regulatory variation that influences gene expression. However, the full extent and nature of regulatory variation remains unknown due to the limited sample sizes that are typically studied, resulting in low statistical power.

I will discuss our ongoing work addressing this limitation for the proteome and the transcriptome in the yeast Saccharomyces cerevisiae. For protein levels, we devised an approach based on extremely large pools of genetically different cells that carry proteins with fluorescent tags. For mRNA levels, we used RNA sequencing to profile gene expression in more than 1,000 recombinant yeast individuals. The statistical power of this dataset is high enough to map thousands of regulatory loci that together account for >70% of the heritability of mRNA levels. Together, these data provide a comprehensive view of how genetic variation influences gene expression.

Mon Sep 24

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Sep 21

## MCFAM Seminar

5:30pm - Vincent Hall 16
Topological Data applied to Finance
Kaisa Taipale - 2018 MCFAM Summer Seminar Students, University of Minnesota
Fri Sep 21

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Science Fiction 2018
##### Abstract:

http://www-users.math.umn.edu/~hopki319/seminar_fall18.html#20180921

Fri Sep 21

## Probability Seminar

2:30pm - Vincent Hall 209
The maximum of the characteristic polynomial for a random permutation matrix
Nicholas Cook, UCLA
##### Abstract:

Let $P$ be a uniform random permutation matrix of size $N$ and let $\chi_N(z)= \det(zI - P)$ denote its characteristic polynomial. We prove a law of large numbers for the maximum modulus of $\chi_N$ on the unit circle, specifically,
$\sup_{|z|=1}|\chi_N(z)|= N^{x_c + o(1)}$
with probability tending to one as $N\to \infty$, for a numerical constant $x_c\approx 0.652$. The main idea of the proof is to uncover an approximate branching structure in the distribution of (the logarithm of) $\chi_N$, viewed as a random field on the circle, and to adapt a well-known second moment argument for the maximum of the branching random walk. Unlike the well-studied \emph{CUE field} in which $P_N$ is replaced with a Haar unitary, the distribution of $\chi_N(z)$ is sensitive to Diophantine properties of the argument of $z$. To deal with this we borrow tools from the Hardy--Littlewood circle method in analytic number theory. Based on joint work with Ofer Zeitouni.

Fri Sep 21

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Sep 21

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Sep 21

9:30am -
CANCELLED

Thu Sep 20

## Student Combinatorics Seminar

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

Thu Sep 20

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Sep 20

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Monotonicity formulas and Type I singularities
Huaidong Cao, Ordway Visitor, Lehigh University
##### Abstract:

In this talk we shall introduce Huisken's monotonicity formula for the mean curvature flow and Perelman's monotonicity formulas for the Ricci flow. We shall discuss their applications, including the role they play in studying Type-I singularities of the flows.

Thu Sep 20

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Random Monomial Ideals
Jay Yang, University of Minnesota
##### Abstract:

I will discuss the contents of my joint paper with Daniel Erman, Random Flag Complexes and Asymptotic Syzygies. In this paper we use the Stanley-Reisner ideals of random flag complexes to construct new examples of Ein and Lazarsfeld's non-vanishing for asymptotic syzygies, and of Ein, Erman, and Lazarsfeld's conjecture on the asymptotic normal distribution of Betti numbers. I will also discuss some work in progress related to the Random Monomial Ideals paper by De Loera, Petrovic, Silverstein, Stasi, and Wilburne.

Thu Sep 20

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory

Thu Sep 20

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Sep 20

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Sep 19

## PDE Seminar

3:30pm - Vincent Hall 570
On sparse bounds for some biparameter operators
Jose Conde Alonso, Department of Mathematics, Brown University
##### Abstract:

The last few years have seen a great deal of work around the concept of sparse domination. This is a technique that allows one to study quantitative inequalities for a wide range of important operators in harmonic analysis in a unified and precise way. We briefly review what sparse domination is and we will explain the very different situation that one en- counters when the operators under study are biparametric, that is, when we consider spaces whose dilations need not be isotropic. Based on joint work (in progress) with Alex Barron, Yumeng Ou and Guillermo Rey.

Tue Sep 18

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Sep 18

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Sep 17

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Lax-Phillips estimates for rank-one groups
Paul Garrett, University of Minnesota
Mon Sep 17

## Topology Seminar

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

Mon Sep 17

## Dynamical Systems

2:30pm - Vinent Hall 570
Careful or colorful: A mathematical model for the evolution of animal ornaments
Danny Abrams, Northwestern
##### Abstract:

Extravagant and costly ornaments (e.g., deer antlers or peacock feathers) are found throughout the animal kingdom. Charles Darwin was the first to suggest that female courtship preferences drive ornament development through sexual selection. In this talk I will describe a minimal mathematical model for the evolution of animal ornaments, and will show that even a greatly simplified model makes nontrivial predictions for the types of ornaments we expect to find in nature.

Mon Sep 17

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Sep 14

## MCFAM Seminar

5:30pm - Vincent Hall 16
How to Get the Most Out of the MFM
MFM 2nd Yr. Student/Alumni Panel, U of M - School of Mathematics - MCFAM
Fri Sep 14

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Ehrhart polynomial of a polytope plus dilating zonotope
Sam Hopkins, University of Minnesota
##### Abstract:

In earlier joint work with Pavel Galashin, Thomas McConville, and Alex Postnikov, we introduced certain directed graphs, depending on a deformation parameter k, whose vertex sets are the weight lattice of a root system. We showed that there is a natural way to label the connected components of these directed graphs across values of k so that the number of points in each connected component is a polynomial in k, which we termed an "Ehrhart-like polynomial" in analogy with the Ehrhart polynomials of lattice polytopes. We conjectured that these Ehrhart-like polynomials have nonnegative integer coefficients. This conjecture prompts us to study the polynomial which counts the number of lattice points in the Minkowski sum of a permutohedron and a dilating regular permutohedron, or more generally in the Minkowski sum of a polytope and a dilating zonotope. We extend Stanley's well-known formula for the Ehrhart polynomial of a zonotope to give a formula for this polynomial. And we then use this formula, together with a subtle integrality property of slices of permutohedra, to give a positive, combinatorial formula for the Ehrhart-like polynomials mentioned above. This is joint work with Alex Postnikov.

Fri Sep 14

## Probability Seminar

2:30pm - Vincent Hall 209
The travel time to infinity in percolation
Wai-Kit Lam, UMN
##### Abstract:

On the two-dimensional square lattice, assign i.i.d. nonnegative weights to the edges with common distribution $F$. For which distributions $F$ is there an infinite self-avoiding path with finite total weight? It has long been known that there is no such infinite path when $F(0) < 1/2$ (there are only finite clusters of zero-weight edges), and there is one when $F(0) > 1/2$ (there is an infinite cluster of zero-weight edges). The critical case, $F(0) = 1/2$, is considerably more difficult due to the presence of finite clusters of zero-weight edges on all scales. In a joint work with M. Damron and X. Wang, we give a necessary and sufficient condition on $F$ for the existence of an infinite finite-weight path, and study the asymptotic behaviors of the first-passage time in the critical case. I will also discuss a recent work with M. Damron and J. Hanson in which we prove some limit theorems for the first-passage time in the critical case on the triangular lattice.

Fri Sep 14

## Lie Theory Seminar

2:30pm - Vincent Hall 313
D-modules, perverse sheaves, and the Riemann-Hilbert correspondence: an overview
Kai-Wen Lan, University of Minnesota
Fri Sep 14

## Student Topology Seminar

1:30pm - Vincent Hall 311
Fomin-Kirillov Algebras, and why we care
Greg Michel
##### Abstract:

In this talk, I'll introduce an interesting family of algebras called the Fomin-Kirillov algebras. We'll explore some basic properties and talk about how better understanding these algebras could lead to some fascinating results in Algebraic Topology.

Fri Sep 14

9:30am -
CANCELLED

Thu Sep 13

## Student Combinatorics Seminar

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

Thu Sep 13

## Colloquium

3:35pm - Vincent Hall 16
Singularities of the Ricci flow and Ricci solitons
Huai-Dong Cao, Lehigh University, Ordway Visitor
##### Abstract:

Understanding formation of singularities has been an important subject in the study of the Ricci flow and other geometric flows. It turns out generic singularities in the Ricci flow are modeled on shrinking Ricci solitons. In this talk, I will discuss some of the recent progress on classifications of shrinking Ricci solitons and their stability/instability with respect to Perelman's $\nu$-entropy.

Thu Sep 13

## Differential Geometry and Symplectic Topology Seminar

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

Thu Sep 13

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory

Thu Sep 13

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Sep 13

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Sep 12

## PDE Seminar

3:30pm - Vincent Hall 570
Estimates of the entropy numbers of the Sobolev embedding near the limit case
Yuri Netrusov, Bristol
##### Abstract:

In 1967 M.Birman and M.Solomyak proved the following remarkable result. Let l,d be positive integers in [1,\infty], and T be the embedding of W^l_p((0,1)^d) to L^q ((0,1)^d). Suppose that 0 < 1/p-1/q < l/d.
Then there are positive constants c_1, c_2 such that for all positive interges k the estimates c_1 k^{-l/d} \leq e_k(T) \leq c_2 k^{-l/d} hold. Here e_k(T) is the k-entropy number of T. Some generalizations and extensions of this result will be given. For instance under some restrictions on the parameters behavior of c_1, c_2
(as function of l/d-1/p+1/q) were investigated.

Tue Sep 11

## Climate Seminar

11:15am - Vincent Hall 570
The Scientific Case for Anthropogenic Warming
Richard McGehee, University of Minnesota
Tue Sep 11

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Sep 10

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Forms and Number Theory

Mon Sep 10

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Fri Sep 07

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Sep 07

## Analysis and PDE Working Seminar

3:35pm - Vincent Hall 206
Sufficient conditions for $C^{1,\alpha}$ parametrization and rectifiability
Silvia Ghinassi, Stony Brook University
##### Abstract:

We provide sufficient conditions for a set or measure in $\mathbb{R}^n$ to be $C^{1,\alpha}$ $d$-rectifiable, with $\alpha \in [0,1]$. The conditions use a Bishop-Jones type square function and all statements are quantitative in that the $C^{1,\alpha}$ constants depend on such a function. Key tools for the proof come from Guy David and Tatiana Toro's parametrization of Reifenberg flat sets (with holes) in the H\"{o}lder and Lipschitz categories.

Fri Sep 07

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Sep 07

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Sep 07

9:30am -
CANCELLED

Thu Sep 06

## Differential Geometry and Symplectic Topology Seminar

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

Thu Sep 06

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory

Thu Sep 06

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Sep 06

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Wed Sep 05

## Commutative Algebra Seminar

10:10am - Vincent Hall 313
Using mixed Gauss--Manin systems to project, restrict, and dualize $A$-hypergeometric systems
Avi Steiner, Purdue
##### Abstract:

Let $A$ be an integer matrix, and assume that its semigroup ring $\mathbb{C}[\mathbb{N} A]$ is normal. I will discuss how to use mixed and dual mixed Gauss--Manin systems, a notion I introduced recently, to compute the holonomic dual of an $A$-hypergeometric system; and to compute, for $F$ a face of the cone of $A$, the projection and restriction of an $A$-hypergeometric system to the coordinate subspace corresponding to $F$.

Tue Sep 04

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Tue Sep 04

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Aug 31

9:30am -
CANCELLED

Tue Aug 28

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Aug 27

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Aug 24

9:30am -
CANCELLED

Wed Aug 22

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Aug 21

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Aug 20

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Aug 17

9:30am -
CANCELLED

Wed Aug 15

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Aug 14

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Aug 13

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Aug 10

9:30am -
CANCELLED

Wed Aug 08

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Aug 07

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Aug 06

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Aug 03

## Combinatorics Seminar

1:30pm - Vincent Hall 113
Combinatorics Seminar
Theo Douvropoulos, IRIF, University of Paris-Diderot
Fri Aug 03

9:30am -
CANCELLED

Thu Aug 02

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Thu Aug 02

## Combinatorics Seminar

11:00am - Vincent Hall 570
Combinatorics Seminar
Jang Soo Kim, Sungkyunkwan University
##### Abstract:

We introduce lecture hall tableaux, which are fillings of a skew Young diagram satisfying certain conditions. Lecture hall tableaux generalize both lecture hall partitions and anti-lecture hall compositions, and also contain reverse semistandard Young tableaux as a limit case. We show that the coefficients in the Schur expansion of multivariate little $q$-Jacobi polynomials are generating functions for lecture hall tableaux. Using a Selberg-type integral we show that the moment of multivariate little $q$-Jacobi polynomials, which is equal to a generating function for lecture hall tableaux of a Young diagram, has a product formula. We also explore various combinatorial properties of lecture hall tableaux. This is joint work with Sylvie Corteel.

Wed Aug 01

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Wed Aug 01

## Special Events and Seminars

10:00am - Vincent Hall 16
REU Final Presentations

Tue Jul 31

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Tue Jul 31

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jul 31

## Special Events and Seminars

10:00am - Vincent Hall 16
REU Final Presentations

Mon Jul 30

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jul 30

## Special Events and Seminars

10:00am - Vincent Hall 16
REU Final Presentations

Fri Jul 27

9:30am -
CANCELLED

Thu Jul 26

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Thu Jul 26

## Combinatorics Seminar

11:00am - Vincent Hall 570
Noncrossing partitions, the Bruhat order, and the cluster complex (joint work with Philippe Biane)
Matthieu Josuat-Verges, University of Paris-East Marne-la-Vallee, CNRS
##### Abstract:

Noncrossing partitions of a real reflection group can be defined as an interval in the absolute order (itself being defined using the reflection length). An observation at the origin of this work is the following: a cover relation in noncrossing partitions give two elements that are comparable in the Bruhat order, but the two orders might agree or disagree on such a pair. This leads to distinguishing two kinds of cover relations in noncrossing partitions, hence two new orders. We study various enumerative properties of these, that leads to nice connection with the cluster complex.

Wed Jul 25

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jul 24

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Tue Jul 24

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jul 23

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Jul 20

9:30am -
CANCELLED

Thu Jul 19

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Wed Jul 18

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jul 17

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Tue Jul 17

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jul 16

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Jul 13

9:30am -
CANCELLED

Thu Jul 12

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Wed Jul 11

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jul 10

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Tue Jul 10

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jul 09

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Jul 06

9:30am -
CANCELLED

Thu Jul 05

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Wed Jul 04

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jul 03

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Tue Jul 03

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jul 02

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Jun 29

9:30am -
CANCELLED

Thu Jun 28

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Wed Jun 27

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jun 26

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Tue Jun 26

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jun 25

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Jun 22

9:30am -
CANCELLED

Thu Jun 21

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Wed Jun 20

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jun 19

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Tue Jun 19

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jun 18

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Jun 15

9:30am -
CANCELLED

Thu Jun 14

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Wed Jun 13

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jun 12

## Special Events and Seminars

3:00pm - Vincent Hall 301
Representation Theory Seminar
TBA
Tue Jun 12

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jun 11

## Combinatorics Seminar

3:30pm - Vincent Hall 206
Wildly Nontransitive Dice
Joe Buhler
##### Abstract:

Nontransitive triples of dice have been known for (at least) 60 years. Let A = {2,6,7}, B = {1,5,9}, C = {3,4,8} denote dice taking each of the three indicated values with probability 1/3. As you can (and should!) check, A dominates B in the sense that when each is rolled the probability that A > B is greater than 1/2. Moreover, B dominates C, and C dominates A, so the dominance relation is non-transitive. To make matters worse, the triple A[2], B[2], C[2] --- where A[2] denotes the sum of two rolls of A, etc. --- is (as you have perhaps already checked) also a nontransitive triple. However, the cyclic dominance order is exactly the reverse of the earlier one. The goal of this talk is to present sets of dice with vastly more peculiar nontransitivity properties.

Mon Jun 11

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Jun 08

9:30am -
CANCELLED

Wed Jun 06

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jun 05

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Jun 04

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri Jun 01

9:30am -
CANCELLED

Wed May 30

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue May 29

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon May 28

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri May 25

9:30am -
CANCELLED

Wed May 23

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue May 22

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon May 21

## Climate Seminar

1:25pm - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Fri May 18

9:30am -
CANCELLED

Tue May 15

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue May 15

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon May 14

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Forms and Number Theory

Mon May 14

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri May 11

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri May 11

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri May 11

9:30am -
CANCELLED

Thu May 10

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu May 10

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Wed May 09

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Topological categories containing the category FI - continuation
Cihan Bahran, University of Minnesota
##### Abstract:

This talk will not depend on any of the previous talks about the local cohomology of FI-modules. One of the flagship applications of FI-modules is on configuration spaces. In several cases, the natural FI-action on PConf(X) extends to an action of a topological category which FI strictly embeds into. The very presence of such an extended action significantly simplifies the associated sequence of representations of symmetric groups on cohomology, and in particular improves the stable ranges.

Tue May 08

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue May 08

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue May 08

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue May 08

## Special Events and Seminars

2:30pm - Ford Hall 130

Tue May 08

## Math Physics Seminar

1:25pm - Vincent Hall 301
Math Physics Seminar

Tue May 08

## IMA Data Science Lab Seminar

1:25pm - Lind 409
Objective functionals of machine learning on graphs and their continuum limits
Dejan Slepcev, Carnegie Mellon University
##### Abstract:

We will discuss variational problems arising in machine learning and their limits as the number of data points goes to infinity. Consider point clouds obtained as random samples of an underlying "ground-truth" measure. Graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points.  Many machine learning tasks, such as clustering and semi-supervised learning, can be posed as minimizing  functionals on such graphs. We consider functionals involving graph cuts, graph laplacians and their limits as the number of data points goes to infinity. We will discuss  the limits of functionals  when the number of data points goes to infinity.   In particular we establish under what conditions the minimizers of discrete problems have a well defined continuum limit.

Tue May 08

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue May 08

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue May 08

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon May 07

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Forms and Number Theory

Mon May 07

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon May 07

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon May 07

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri May 04

## MCFAM Seminar

4:30pm - Vincent Hall 16
MCFAM Seminar

Fri May 04

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Gale-Robinson quivers, representations, and combinatorial formulas
Max Glick, Ohio State
##### Abstract:

Gale-Robinson sequences were one of the first examples of the Laurent phenomenon. Moreover, the associated quivers relate to the dimer model from physics. We investigate a family of representations of these quivers that are geared towards providing concrete information about the corresponding cluster algebras. In this way, we provide a representation theoretic explanation for known combinatorial formulas for the Gale-Robinson sequence and also obtain similar formulas for several other cluster variables. This is joint work with Jerzy Weyman.

Fri May 04

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri May 04

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri May 04

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Tatiana Yarmola, J.P. Morgan AG
Fri May 04

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri May 04

## MathCEP Seminar

11:15am - Vincent Hall 113
MathCEP Seminar

Fri May 04

9:30am -
CANCELLED

Thu May 03

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu May 03

## Colloquium

3:30pm - Vincent Hall 16
Fractal solutions of dispersive PDE on the torus
Burak Erdogan, Department of Mathematics, University of Illinois
##### Abstract:

In this talk we discuss qualitative behavior of certain solutions to linear and nonlinear dispersive partial differential equations such as Schrodinger and Korteweg-de Vries equations. In particular, we will present results on the fractal dimension of the solution graph and the dependence of solution profile on the algebraic properties of time.

Thu May 03

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Bochner-Kahler metrics (after R. Bryant)
Rui Loja Fernandes - Ordway Visitor, UIUC
##### Abstract:

In a seminal paper, R. Bryant gave a local description of Bochner-Kahler metrics and a classification of germs of such metrics. In this talk I will sketch a new approach to this classification using the theory of integrability of Lie algebroids. It provides new insight and allows for more precise results, extending the work of Bryant. Our approach can also be used to solve other geometric classification problems (e.g., symplectic connections with special holonomy). This is on-going joint work with Ivan Struchiner (U Sao Paulo, Brazil).

Thu May 03

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu May 03

## Ordway Lecture Series

10:10am - Vincent Hall 16
p-adic Hodge theory and homotopy theory
Bhargav Bhatt, University of Michigan - Ann Arbor
##### Abstract:

In my colloquium talk on 4/26, I discussed the following result, giving a weak analogue of Hodge theory with torsion coefficients: if a smooth and proper complex variety X specializes to a smooth and proper variety X_p in characteristic p, then the mod p singular cohomology of X is controlled by the de Rham cohomology of X_p. The key innovation of this work is the construction of a p-adic cohomology theory that interpolates between known cohomology theories in p-adic geometry (such as p-adic etale cohomology and de Rham cohomology). In this talk, I shall discuss this construction and explain why it is closely related to certain periodicity theorems (such as Bott's and Bokstedt's) in homotopy theory. Joint work with Matthew Morrow and Peter Scholze.

Thu May 03

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed May 02

## PDE Seminar

3:35pm - Vincent Hall 570
A Phase Field Model for Thin Elastic Structures with Topological Constraint
Patrick Dondl, University of Freiburg, Germany
##### Abstract:

With applications in the area of biological membranes in mind, we consider the problem of minimizing Willmores energy among the class of closed, connected surfaces with given surface area that are confined to a fixed container. Based on a phase field model for Willmores energy originally introduced by de Giorgi, we develop a technique to incorporate the connectedness constraint into a diffuse interface model of elastic membranes. Our approach uses a geodesic distance function associated to the phase field to discern different connected components of the support of the limiting mass measure. We obtain both a suitable compactness property for finite energy sequences as well as a Gamma-convergence result. Furthermore, we present computational evidence for the effectiveness of our technique. The main argument in our proof is based on a new, natural notion to describe convergence of phase fields.

Wed May 02

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed May 02

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Algebraic Representation Theory Seminar

Tue May 01

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue May 01

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue May 01

## Topology Seminar

2:30pm - Vincent Hall 2
Edge stabilization in the homology of graph braid groups
Ben Knudsen, Harvard University
##### Abstract:

We discuss a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. Through these maps, the homology of the configuration spaces forms a module over the polynomial ring generated by the edges of the graph, and we show that this module is finitely generated, implying eventual polynomial growth of Betti numbers over any field. Moreover, the action lifts to an action at the level of singular chains, which contains strictly more information; indeed, we show that this differential graded module is almost never formal over the ring of edges. These results, along with numerous calculations, arise from consideration of an explicit chain complex, which is a structured enhancement of a cellular model first considered by Swiatkowski. We arrive at this model through a local-to-global approach combining ideas from factorization homology and discrete Morse theory. This is joint work with Byung Hee An and Gabriel Drummond-Cole.

Tue May 01

## Special Events and Seminars

2:30pm - Ford Hall 130

Tue May 01

## Math Physics Seminar

1:25pm - Vincent Hall 301
STEERING A PARTICLE ON A MATHEMATICALLY SMOOTH SURFACE
Mike Hennessey, University of St. Thomas
##### Abstract:

We consider the general problem of steering an infinitesimal propelled and steerable particle traversing on a mathematically smooth (vs. frictionless) surface, analogous to propelled skiing on the slopes where both the speed and body yaw rate serve as inputs to the system and lateral motion is not allowed, i.e. through a no side-slip condition.
More specifically, focus is on derivation of relevant state equations in control input form, numerical and visual confirmation of state equation accuracy through specific simulations, and exploring interesting approaches to nonholonomic path planning and associated numerical simulation and visualization. Given the state equations (3rd order), in the interests of practical validation, they were exercised by considering motion on a number of smooth surfaces. The surfaces were selected for a variety of reasons, such as: the resulting qualitative trajectory is known a priori, there exists an opportunity to check numerical results with respect to previous results, or the surfaces are iconic and/or are geometrically rich.

Nonholonomic steering on the surface is a very interesting and challenging problem and several approaches are investigated: (1) steering using sinusoids (detailed), (2) steering on a trajectory, and (3) "drive-and-turn" (valid in this case). Prior to implementing the steering with sinusoids algorithm, it was necessary to transform the system into "one-chained" form. The first step entailed conversion to an approximate one-chained form model that possesses a certain structure, from which the process established by Murray et. al. can be successfully launched, where two special smooth scalar functions of the states are sought that possess special relationships to Lie-related distribution spaces associated with the control input vectors. Inputs are then transformed as well via specialized Lie derivatives. It was demonstrated through simulation that steering to an arbitrary system state on a faceted surface can be accomplished with sinusoidal inputs in only one maneuver set (i.e. maneuver A & B). Using this fact, the work presented culminates with steering to an arbitrary system state on a smooth surface that can be accomplished by essentially iterating on a steering algorithm that assumes the particle is on a plane tangent to the smooth surface at the point of interest. In this regard, it is shown that a sequence of maneuver sets (A_i, B_i) converges rather quickly in the example demonstrated.

Tue May 01

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Genetics of mRNA and protein expression in large yeast populations
Frank Albert, University of Minnesota, Twin Cities
##### Abstract:

Genetic variation among individuals is an important source of phenotypic variation within species. Many of these genetic effects are due to regulatory variation that influences gene expression. However, the full extent and nature of regulatory variation remains unknown due to the limited sample sizes that are typically studied, resulting in low statistical power. I will discuss our ongoing work addressing this limitation for the proteome and the transcriptome in the yeast Saccharomyces cerevisiae. For protein levels, we devised an approach based on extremely large pools of genetically different cells that carry proteins with fluorescent tags. For mRNA levels, we used RNA sequencing to profile gene expression in more than 1,000 recombinant yeast individuals. The statistical power of this dataset is high enough to map thousands of regulatory loci that together account for >70% of the heritability of mRNA levels. Together, these data provide a comprehensive view of how genetic variation influences gene expression.

Tue May 01

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Zachi Attia, Mayo Clinic
Tue May 01

## Analysis and PDE Working Seminar

1:25pm - B45 Tate Hall
Analysis & PDE Working Seminar

Tue May 01

## Climate Seminar

11:30am - 570 Vincent Hall
Climate Change Seminar (Bonny - ATTEND)
Richard McGehee
Tue May 01

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue May 01

## Ordway Lecture Series

10:10am - Vincent Hall 16
The direct summand conjecture and its derived variant
Bhargav Bhatt, University of Michigan - Ann Arbor
##### Abstract:

In the late 60's, Hochster formulated the direct summand conjecture (DSC) in commutative algebra, which is the following innocuous looking assertion: a finite extension A --> B of commutative rings admits an A-module splitting if A is regular and noetherian. A few years later, Hochster himself proved the DSC when the ring contains a field; this and related ideas eventually had a significant impact on the development of the theory of F-singularities.

In the mixed characteristic setting, the case of dimension <= 3 was settled by Heitmann in the 90's. The general case was resolved beautifully by Yves Andr\'e in late 2016 using perfectoid geometry.

In this talk, I'll present a simplification of Andr\'e's proof of DSC. I will also explain why similar ideas help establish a derived variant of the DSC put forth by de Jong; the latter roughly states that regular rings have rational singularities. One of my main goals in this talk to explain why passing from a mixed characteristic ring to a perfectoid extension is a useable analogue of the passage to the perfection (direct limit over Frobenius) in characteristic p.

Tue May 01

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Tue May 01

## Special Events and Seminars

8:30am - Vincent Hall 570
Senior Honors Presentations
Senior Honors Presentations
##### Abstract:

8:30- 8:50, Owen Levin, working title "Approximation Algorithms for Network Connectivity," adviser
Professor Reiner
9- 9:20, Maria Gilbert, working title "Hurwitz Actions in Complex Reflection Groups", adviser Professor Reiner
9:30-9:50, Ryan Vogt, "Detection of Non-Symmetric Balanced Configurations", adviser Professor Moeckel
10-10:20, Ian McMeeking, "Computing With Noncongruence Subgroups", adviser Professor Brubaker
10:30-10:50, Bat-Orgil Batsaikhan, Generative Capsule Network", adviser Professor Lerman.
11-11:20, Elena Hafner, Face Structure and Volume of the Birkhoff Polytope", adviser ProfessorMusiker

Everyone welcome. Honors undergraduate math students present a short account of their work.

Mon Apr 30

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Curiosities of exotic eigenfunction expansions
Mon Apr 30

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Optical phenomena in layered 2D materials
Matthias Maier, University of Minnesota
##### Abstract:

In the past few years the dream of manipulating the laws of optics at will
has evolved into a reality with the use of metamaterials. These structures
have made it possible to observe aberrant behavior like no refraction, and
negative refraction. The level of control of the path and dispersion of
light that is offered by metamaterials is of fundamental interest and can
lead to exciting applications. In particular, plasmonic metamaterials offer
significant flexibility in tuning permittivity or permeability values. This
advance has opened the door to novel devices and applications that include
tunable metamaterials, optical cloaking, and subwavelength focusing lenses.
There is a compelling need for controllable numerical schemes which, placed
on firm mathematical grounds, can reliably describe optical phenomena in a
variety of geometries.

In this talk we present analytical and numerical results for the simulation
of optical phenomena on 2D materials and layered structures. In particular,
we introduce a homogenization theory of layered heterostructures to design
novel devices, and present a number of applications of the framework to
optical device simulations. Aspects of the numerical treatment such as
absorbing perfectly matched layers, local refinement and a-posteriori error
control are discussed as well.

Mon Apr 30

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Apr 30

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon Apr 30

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri Apr 27

## MCFAM Seminar

5:30pm - Tate Hall 101
MCFAM Seminar

Bio:

Fri Apr 27

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Young tableaux, Kazhdan-Lusztig cells, and Springer fibers
Dongkwan Kim, MIT
##### Abstract:

The generalized Robinson-Schensted algorithm, introduced by J.-Y. Shi, is a surjection from the affine symmetric groups to the pairs of row-standard Young tableaux of the same shape. It was used to prove the conjecture of Lusztig on the enumeration of left cells in affine symmetric groups. On the other hand, combinatorics of row-standard Young tableaux is also closely related to the affine paving of Springer fibers. In this talk, I briefly recall these concepts and how they are related, and focus on generalizations of this picture to other classical types.

Fri Apr 27

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Apr 27

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Apr 27

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Guy-vanie Miakonkana, Travelers Insurance
Fri Apr 27

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Apr 27

## MathCEP Seminar

11:15am - Vincent Hall 113
Patterns of Gendered Performance Difference in Introductory STEM Courses
Journal Article Discussion
##### Abstract:

We will discuss data compiled from the University of Michigan in "Patterns of Gendered Performance Difference in Introductory STEM Courses. This data looks at student performance as measured by grades in 116 large courses at the University of Michigan and examines performance by gender and discipline. The authors find that most STEM courses impose a grade penalty on all students (grades in these courses are lower than their average grades in all other courses), and the grade penalty is greater for females than males. This gendered performance difference does not exist in all disciplines. The authors hypothesize that evaluation methods used in STEM lectures in combination with stereotype threat may be responsible for these differences.

Fri Apr 27

9:30am -
CANCELLED

Thu Apr 26

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Apr 26

## Colloquium

3:30pm - Vincent Hall 16
Phase transitions and conic geometry
Ordway Visitor - Joel Tropp
##### Abstract:

A phase transition is a sharp change in the behavior of a mathematical model as one of its parameters changes. This talk describes a striking phase transition that takes place in conic geometry. First, we will explain how to assign a notion of "dimension" to a convex cone. Then we will use this notion of "dimension" to see that two randomly oriented convex cones share a ray with probability close to zero or close to one. This fact has implications for many questions in signal processing. In particular, it yields a complete solution of the "compressed sensing" problem about when we can recover a sparse signal from random measurements. This talk is designed for a general mathematical audience.

Based on joint works with Dennis Amelunxen, Martin Lotz, Mike McCoy, and Samet Oymak.

Thu Apr 26

## IMA Data Science Lab Seminar

3:30pm - Vincent 16
Phase transitions and conic geometry
Joel Tropp, California Institute of Technology
##### Abstract:

A phase transition is a sharp change in the behavior of a mathematical model as one of its parameters changes. This talk describes a striking phase transition that takes place in conic geometry. First, we will explain how to assign a notion of "dimension" to a convex cone. Then we will use this notion of "dimension" to see that two randomly oriented convex cones share a ray with probability close to zero or close to one. This fact has implications for many questions in signal processing. In particular, it yields a complete solution of the "compressed sensing" problem about when we can recover a sparse signal from random measurements. This talk is designed for a general mathematical audience.

Based on joint works with Dennis Amelunxen, Martin Lotz, Mike McCoy, and Samet Oymak.

Thu Apr 26

## Colloquium

2:30pm - Vincent Hall 16
Bounding torsion in cohomology
Ordway Visitor Bhargav Bhatt, University of Michigan
##### Abstract:

The integral cohomology groups of a complex algebraic variety are one of the most fundamental invariants associated to the variety. The ranks of these groups are well understood in terms of the equations defining the variety, thanks to Hodge theory. However, the torsion tends to be more "transcendental" in nature and is not easily accessible via algebraic techniques. Torsion cohomology classes have played a pivotal role in many recent advances in number theory, algebraic geometry, and representation theory, so it is important to better understand torsion from an algebraic perspective. In this talk, I'll discuss my recent work with Morrow and Scholze that explains how to bound the torsion explicitly in terms of the equations defining the variety.
________________________________

Thu Apr 26

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Apr 26

## Differential Geometry and Symplectic Topology Seminar

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

Thu Apr 26

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Apr 26

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 16
Geometric Analysis Learning Seminar

Thu Apr 26

## Special Events and Seminars

9:00am - Vincent Hall 570
Senior Honors Presentations
Senior Honors Presentations
##### Abstract:

9-9:20, Kelly Catlin, "Finding an Optimal Velocity for a Race" , adviser Professor Mori
9:30-9:50, Mark Richard, "On Random Schrodinger Operators" , adviser Professor Chen
10-10:20, Paul Aarsvold, "Manifolds and the Shape of the Universe", adviser Professor Rogness

Everyone welcome. Honors undergraduate math students present a short account of their work.

Wed Apr 25

## PDE Seminar

3:35pm - Vincent Hall 570
Scattering below the ground state for nonlinear Schrödinger equations
Jason Murphy
##### Abstract:

The ground state solution to the nonlinear Schrödinger equation (NLS) is a global, non-scattering solution that often provides a threshold between scattering and blowup. In this talk, we will discuss new, simplified proofs of scattering below the ground state threshold (joint with B. Dodson), as well as some extensions to other models of NLS (joint with R. Killip, M. Visan, J. Zheng, as well as with C. Miao and J. Lu).

Wed Apr 25

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Apr 25

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Topological categories containing the category FI
Cihan Bahran, University of Minnesota
##### Abstract:

This talk will not depend on any of the previous talks about the local cohomology of FI-modules. One of the flagship applications of FI-modules is on configuration spaces. In several cases, the natural FI-action on PConf(X) extends to an action of a topological category which FI strictly embeds into. The very presence of such an extended action significantly simplifies the associated sequence of representations of symmetric groups on cohomology, and in particular improves the stable ranges.

Tue Apr 24

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Apr 24

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Apr 24

## Special Events and Seminars

2:30pm - Ford Hall 130
Cyclic Groups and Partitions
##### Abstract:

A partition is a way of writing n as the sum of positive integers. While working in the cyclic of the finite group order n, it is possible to partition the entire group into a fixed size such that the partitions are equivalent to 0 modulo n. Since there is a direct bijective correspondence between Young Diagrams, cyclic partitions, and Gaussian binomial coefficients, it will be show that these box-partitions can be counted by the sum of specific coefficients within the Gaussian binomial coefficients.

Tue Apr 24

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Sketchy decisions: Low-rank convex matrix optimization with optimal storage
Joel Tropp, California Institute of Technology
##### Abstract:

Convex matrix optimization problems with low-rank solutions play a fundamental role in signal processing, statistics, and related disciplines. These problems are difficult to solve because of the cost of maintaining the matrix decision variable, even though the low-rank solution has few degrees of freedom. This talk presents an algorithm that provably solves these problems using optimal storage. The algorithm produces high-quality solutions to large problem instances that, previously, were intractable. Joint work with Volkan Cevher, Roarke Horstmeyer, Quoc Tran-Dinh, Madeleine Udell, and Alp Yurtsever.

Bio
Joel A. Tropp is Steele Family Professor of Applied & Computational Mathematics at the California Institute of Technology. He earned the Ph.D. degree in Computational Applied Mathematics from the University of Texas at Austin in 2004. His research centers on signal processing, numerical analysis, and random matrix theory. Prof. Tropp won a PECASE in 2008, and he has received society best paper awards from SIAM in 2010, EUSIPCO in 2011, and IMA in 2015. He has also been recognized as a Highly Cited Researcher in Computer Science each year from 20142017.

Tue Apr 24

## Math Physics Seminar

1:25pm - Vincent Hall 301
Toward a classification of semidegenerate and degenerate 3D superintegrable systems
W. Miller, Jr.
##### Abstract:

Superintegrable systems of 2nd order in 3 dimensions with exactly 3-parameter potentials are intriguing objects. Next to the nondegenerate 4-parameter potential systems they admit the maximum number of symmetry operators, but their symmetry algebras don't close under commutation and not enough is known about their structure to give a complete classification. Some examples are known for which the 3-parameter system can be extended to a 4th order superintegrable system with a 4-parameter potential and 6 linearly independent symmetry generators. Here, we use B\^ocher contractions of the conformal Lie algebra so(5,C) to itself to generate a large family of 3-parameter systems with 4th order extensions, on a variety of manifolds, all from B\^ocher contractions of a single generic'' system on the 3-sphere. We give a contraction scheme relating these systems. The results have myriad applications for finding explicit solutions for both quantum and classical systems as well as a classification of degenerate systems with less than 3-parameter potentials.

Tue Apr 24

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Apr 24

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Apr 24

## Ordway Lecture Series

10:10am - Vincent Hall 16
Introduction to perfectoid spaces
Bhargav Bhatt, University of Michigan, Ann Arbor
##### Abstract:

Perfectoid geometry is a relatively newly uncovered corner of arithmetic geometry. It provides a context where we can fruitfully treat a prime number like a variable, thus opening the door to systematically applying algebro-geometric techniques to problems in arithmetic. Consequently, these spaces have already solved important problems not only in number theory, but also in algebraic geometry, representation theory, commutative algebra, and even homotopy theory. In this talk, I will introduce the basic notions of perfectoid geometry. The goal is to introduce the background necessary to follow the applications discussed in the following talks.

Tue Apr 24

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Apr 23

## Applied and Computational Math Colloquium

3:35pm - Keller Hall 3-180
Applied random matrix theory
Joel Tropp, Steele Family Professor of Applied & Computational Mathematics
##### Abstract:

Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that balance these criteria. This talk offers an invitation to the field of matrix concentration inequalities and their applications.

Mon Apr 23

## IMA Data Science Lab Seminar

3:35pm - Keller 3-180
Applied Random Matrix Theory
Joel Tropp, California Institute of Technology
##### Abstract:

Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that balance these criteria. This talk offers an invitation to the field of matrix concentration inequalities and their applications.

Bio
Joel A. Tropp is Steele Family Professor of Applied & Computational Mathematics at the California Institute of Technology. He earned the Ph.D. degree in Computational Applied Mathematics from the University of Texas at Austin in 2004. His research centers on signal processing, numerical analysis, and random matrix theory. Prof. Tropp won a PECASE in 2008, and he has received society best paper awards from SIAM in 2010, EUSIPCO in 2011, and IMA in 2015. He has also been recognized as a Highly Cited Researcher in Computer Science each year from 20142017.

Mon Apr 23

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Forms and Number Theory
Doga Guctenkorkmaz, University of Minnesota
Mon Apr 23

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Apr 23

## Topology Seminar

2:30pm - Vincent Hall 6
The Orlik-Terao algebra and the cohomology of configuration spaces
Nick Proudfoot, University of Oregon
##### Abstract:

The Orlik-Terao algebra is the subalgebra of all rational
functions in n variables generated by 1/(x_i - x_j). I will explain
how to use topological techniques to understand this algebra as a
graded representation of the symmetric group. I will also describe
two different connections (one proven and one conjectural) between
this algebra and the cohomology of configuration spaces.

Mon Apr 23

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon Apr 23

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri Apr 20

## MCFAM Seminar

5:30pm - Vincent Hall 16
Introduction to Quantile Regression and its Applications in Health Care Cost Data Analysis
Lan Wang, University of Minnesota School of Statistics
##### Abstract:

Analysis of health care cost data is often complicated by a high level of skewness, heteroscedastic variances and the presence of missing data. Most of the existing literature on cost data analysis have been focused on modeling the conditional mean. We will introduce quantile regression techniques for estimating the conditional quantiles health care cost data. The quantile regression framework allows us to obtain a more complete picture of the effects of the covariates on the health care cost, and is naturally adapted to the skewness and heterogeneity of the cost data. The framework we introduce can handle missing data and large number of covariates.

Fri Apr 20

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Dual braid monoids, Koszul algebras, and clusters
##### Abstract:

The dual braid monoid of a finite Coxeter group W is a homogeneous monoid with group of fractions the classical braid group attached to W. It was defined in general by David Bessis, and possesses nice algebraic and combinatorial properties. In this talk we will study the algebra of this monoid, and show that it belongs to the class of Koszul algebras. Moreover, positive elements of the cluster complex attached to W naturally index a family in the "Koszul dual" of this algebra. These elements conjecturally form a basis of this dual algebra.

This is joint work with Matthieu Josuat-Vergès and Jang Soo Kim.

Fri Apr 20

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Apr 20

## Probability Seminar

2:30pm - Vincent Hall 311
PDEs and semi-supervised learning on random geometric graphs
Jeff Calder, UMN
##### Abstract:

Semi-supervised learning refers to machine learning algorithms that make use of both labeled data and unlabeled data for learning tasks. Examples include problems such as speech recognition, website classification, and discovering folding structure of proteins. In many problems there is an abundance of unlabeled data, while labeled data often requires expert labeling and is expensive to obtain. This has led to a resurgence of semi-supervised learning techniques, which use the topological or geometric properties of large amounts of unlabeled data to aid the learning task. In this talk, I will discuss some new rigorous PDE scaling limits for semi-supervised learning on random geometric graphs.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.0px; font: 13.0px Arial; color: #232323; -webkit-text-stroke: #232323}span.s1 {font-kerning: none}

Fri Apr 20

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
A Path to Industry: Some things you can do today to succeed tomorrow
Tatiana Yarmola, J.P. Morgan AG
##### Abstract:

This talk highlights a path to the field of modeling. Models are quantitative representations of real world phenomena and are used in many industries and business functions. People with STEM degrees have abilities to understand, evaluate and build models. Yet, there seems to be a lot of confusion on how to become the chosen one and get a job in the area. "A path to industry" explains which skills, beyond quantitative, an employer may be looking for, and gives examples of things you can start doing now to reframe your academic experience and stand out from the competition. It also encourages you to treat your career as an ongoing research project.

Bio
Tanya investigates model risks at JP Morgan Chase. As a model reviewer, she evaluated conceptual soundness, data inputs and implementations of models within the bank. At the UNECE Statistical Division, she assisted with strategic developments in the modernization of statistical production in the public sector. Her projects included gathering specifications for a big data sandbox, editing big data proposals, improving computations in the UNECE statistical database, and co-organizing a statistical data collection meeting. As a postdoctoral researcher in mathematics and physics, she established the original rigorous proofs of important statistical properties of Markov processes modeling gas behavior.

Fri Apr 20

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Apr 20

## MathCEP Seminar

11:15am - Vincent Hall 113
MathCEP Seminar

Thu Apr 19

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Apr 19

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Thu Apr 19

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
How to Make a Black Hole
Xianliang An, University of Toronto
##### Abstract:

Black holes are predicted by Einstein's theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being. In this talk, with tools from hyperbolic PDE, quasilinear elliptic equations, geometric analysis and dynamical systems, we will prove that, through a nonlinear focusing effect, initially low-amplitude and diffused gravitational waves can give birth to a black hole region in our universe. This result extends the 1965 Penroses singularity theorem and it also proves a conjecture of Ashtekar on black-hole thermodynamics. Open problems and new directions will also be discussed.

Thu Apr 19

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Apr 19

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Apr 18

## PDE Seminar

3:35pm - Vincent Hall 570
The Landis conjecture for elliptic operators
Luca Rossi, EHESS, Paris
##### Abstract:

The Landis conjecture, proposed in the 80s, states that if a solution of an elliptic equation decays faster than a suitable exponential then it must be identically equal to zero.This conjecture has been disproved by Meshkov in the case of complex-valued functions, but it remains open in the real case. In this talk, I will recall some partial results obtained by Kenig and collaborators. Next, I will present the proof of the conjecture in dimension one and its application to the radial case. Finally, I will consider the restriction to positive solutions and to operators with positive generalized principal eigenvalue.

Wed Apr 18

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Apr 18

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Topological categories containing the category FI- cancelled
Cihan Bahran, University of Minnesota
##### Abstract:

This talk will not depend on any of the previous talks about the local cohomology of FI-modules. One of the flagship applications of FI-modules is on configuration spaces. In several cases, the natural FI-action on PConf(X) extends to an action of a topological category which FI strictly embeds into. The very presence of such an extended action significantly simplifies the associated sequence of representations of symmetric groups on cohomology, and in particular improves the stable ranges.

Tue Apr 17

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Apr 17

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Apr 17

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue Apr 17

## Special Events and Seminars

2:30pm - Ford Hall 130
Quivers, Representations, and Gabriel's Theorem
Nick White
##### Abstract:

Gabriels theorem states that a connected quiver has finite representation type if and only if its underlying graph has Dynkin type A, D, or E, and that for such quivers, the isoclasses of indecomposable representations are in bijection with the positive roots of the quivers associated quadratic form. The goal of this talk is to introduce some results that motivate Gabriels theorem and give an overview of the proof. Along the way, I will develop some language to talk about representations, including short exact sequences and projective resolutions.

Tue Apr 17

## Math Physics Seminar

1:25pm - Vincent Hall 301
Symmetry Through the Ages
Jimmy Broomfield
##### Abstract:

In this talk, we explore the topic of symmetry viewed in the context of key mathematical breakthroughs. Historical stories will be accompanied by mathematical examples to shed light on what we mean by symmetry. In our journey, we will meet the likes of Évariste Galois, Sophus Lie, Felix Klein, and Emmy Noether.

Tue Apr 17

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Population Genomics of Host-microbiome Interactions
Ran Blekhman, University of Minnesota, Twin Cities
##### Abstract:

The composition of the microbial communities that colonize the human body varies widely across individuals and populations, and has been associated with numerous host traits and diseases. Although the microbiome is influenced by environmental factors, a strong host genetic factor is also expected to control the interaction between humans and the microbiome. Understanding the relative role of genetic and environmental factors in host-microbiome interactions is a central goal in human disease research. In my talk, I describe research in my lab, which is based on the hypothesis that the microbiome can be considered a quantitative trait, and thus we can directly map host genomic factors controlling the variation in the microbiome, as well as identify individual host genes and pathways that are regulated by the microbiome. I will describe our effort to create a systems-level view of the molecular interactions between host genes and microbial taxa, genes, and pathways in the gut; a characterization of how microbiome dynamics and taxa are controlled by host genetic variation; and a description of the mechanism with which the microbes regulate host genes. These results shed light on the interplay between human genomics and the microbiome, explain how this interaction affects disease, and would enable development of microbiome-based therapeutics and diagnostics that improve human health.

Tue Apr 17

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Apr 17

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Apr 17

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Apr 16

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Interatomic Potentials from First Principles
Christoph Ortner (Warwick)
##### Abstract:

Quantum chemistry provides accurate and transferrable models for interatomic forces from electronic structure, but their extreme computational cost makes them unsuitable for simulating complex material phenomena such as plasticity, cracking, or embrittlement, that span many length- and time-scales. The canonical alternative to study atomistic mechanisms in materials are interatomic potentials (IPs), which are empirical models with comparatively poor accuracy and transferrability.

Three seminal papers (Behler & Parinello, 2007; Bartok et al, 2010; Shapeev, 2016) began to treat the construction of IPs as an approximation problem (or, "machine learning", to employ the modern term), instead of a modelling problem, which creates both a need and an opportunity for a mathematical theory of IPs. In this talk I will try to outline such a theory. starting from a quantum chemistry model (for simplicity I will focus on tight-binding), I will make a sequence of controlled approximations to eventually arrive at an interatomic potential with tunable cost/accuracy ratio.

This talk is based on ongoing (incomplete) work with Genevieve Dusson (Warwick), Gabor Csanyi (Cambridge) and Cas van der Oord (Cambridge).

Mon Apr 16

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
On zeroes of constant terms of Eisenstein series
Dev Hegde, University of Minnesota
Mon Apr 16

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Apr 16

## Dynamical Systems

2:30pm - Vincent Hall 20
The Foucault Pendulum -- with a Twist
Rick Moeckel, University of Minnesota
##### Abstract:

A Foucault pendulum is supposed to precess in a direction opposite to the earth's rotation, but nonlinear terms in the equations of motion can also produce precession. So what are you actually seeing when you watch one ? The talk will describe the motion of a nonlinear, spherical pendulum on a rotating planet. It turns out that the problem on a fixed energy level reduces to the study of a monotone twist map of an annulus. For certain values of the parameters, this leads to existence proofs for orbits which do not precess or else precess in the wrong direction. In fact there will be nonprecessing periodic solutions which return to their initial state after swinging back and forth just once. For pendula of modest size, these nonprecessing periodic solutions can be very nearly planar.

Mon Apr 16

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri Apr 13

## MCFAM Seminar

5:30pm - Vincent Hall 16
Probability Space of Regression Models and Its Applications to Stress Case Scenario Testing
Validimir Ladyzhets, University of Connecticut School of Business & Lava Consulting Services LLC
##### Abstract:

In this presentation we discuss a modeling framework that has developed and tested for carrying out a feasibility study to find out whether the macroeconomic factors suggested by the Federal Reserve Bank (FRB) can be used to build robust and meaningful regression models for estimating time development of bank holding companies (BHC) revenues and/or losses. In the most general terms, this framework allows one to create a probability space of regression models, where models probability measure is defined by a regression model performance. The approach is illustrated by showing how a probability space of regression models can be created and used for estimating operational risk losses against three supervisory scenarios (supplied by FRB) - baseline, adverse, and severely adverse  for time development of key macroeconomic factors.

Bio: Dr. Vladimir Ladyzhets works in the field of Risk Modeling. He has has served in a variety of management positions for more than 15 years including: Banco Santander, GE Financial Services, Lava Consulting Services LLC, Lincoln Financial Group Babson Capital Management, Travelers, and Ernst & Young. In these firms he has focused on operational risk management, credit analytics, quantitative risk management, and predictive modeling. Since 2013 he has also been an adjunct professor at the University of Connecticut Business School where he teaches graduate courses in financial risk management. Dr. Ladyzhets holds a PhD in Applied Mathematics from the Novosibirsk State University.

Fri Apr 13

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar

Fri Apr 13

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Apr 13

## Probability Seminar

2:30pm - Vincent Hall 311
The geometry of pure states in spherical spin glasses
Eliran Subag, New York University
##### Abstract:

One of the central ideas in the physical theory of mean-field spin glasses developed in the 80s was that the system decomposes into pure states', organized in an ultrametric structure. In his seminal work Talagrand (2010) proved for a wide class of models the existence of such a decomposition -- a sequence of subsets on which the Gibbs measure asymptotically concentrates. Panchenko (2013) established the famous ultrametricity conjecture, implying, in particular, that those subsets are organized in a certain hierarchical structure.

In the context of the spherical models, I will describe a new geometric picture for the above, in which the hierarchy is expressed through a tree of nested spherical sections. In particular, the pure states concentrate on spherical bands corresponding to the leaves of this tree.

Fri Apr 13

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
A Field Guide to Data Science in the Wild
Dan Atkins, Optum
Fri Apr 13

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Apr 13

## MathCEP Seminar

11:15am - Vincent Hall 113
Flipping 5251: A survey of the literature and my experiences flipping an upper-division math course
Melissa Lynn, University of Minnesota
##### Abstract:

"Flipped" course structures, where in-class and out-of-class activities are switched, have become increasingly popular as methods of incorporating active learning. Although flipped structures are most commonly used in Precalculus and Calculus courses, they can, in theory, be adapted for any math course. I will discuss my experiences flipping an upper-division math course and connect this with the literature on flipped classes, focusing on common components of flipped courses and their effectiveness. Reviewing the existing literature, in conjunction with my own experience, provides both evidence that flipping is effective and theories about why it is effective.

Thu Apr 12

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Apr 12

## Ordway Lecture Series

3:30pm - Vincent Hall 364
Hankel Transforms, Langlands Functoriality and Functional Equation of Automorphic L-functions (III)
Bao Chau Ngo, University of Chicago, Distinguished Ordway Visitor of UMN
Thu Apr 12

## Colloquium

2:30pm - Vincent Hall 16
Perfectoid spaces, homological conjectures, and singularities in mixed characteristic
Linquan Ma, University of Utah
##### Abstract:

The homological conjectures have been a focus of research in commutative algebra since 1960s. They concern a number of interrelated conjectures concerning various homological properties of commutative rings to their internal ring structures. These conjectures had largely been resolved for rings that contain a field, but several remained open in mixed characteristic---until recently Yves Andre proved Hochster's direct summand conjecture and the existence of big Cohen-Macaulay algebras, which lie in the heart of the homological conjectures. The main new ingredient in the solution is to systematically use Scholze's theory of perfectoid spaces, which leads to many further developments in the study of mixed characteristic singularities. For example, using perfectoid algebras and big Cohen-Macaulay algebras, we can define the mixed characteristic analog of rational/F-rational and log terminal/F-regular singularities, and they turn out to have many applications to singularities over arithmetic families (this is based on recent joint work with Karl Schwede). In this talk, we will survey all these results.

Thu Apr 12

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Apr 12

## Colloquium

1:30pm - Vincent Hall 570
"Matryoshka Dolls and Tinkertoys: Calabi-Yau Manifolds and Supersymmetry"
Charles Doran, University of Alberta
##### Abstract:

The geometry of Calabi-Yau manifolds and supersymmetry are key ingredients in string theory. We will take a non-traditional point of view on both of these. The hereditary structure of nested Calabi-Yau manifolds underlies string dualities and motivates an algebraic reinterpretation. Dimensional reduction of supermultiplets produces a discrete scaffolding (Adinkra graphs) that nevertheless possesses an emergent form of geometry. Surprisingly, we find that supermultiplets themselves bear the stamp of Calabi-Yau geometry. Our proof of this uses work of H.S.M. Coxeter inspired by a woodcut by M.C. Escher. The talk is designed to be broadly accessible to graduate students.

Thu Apr 12

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Apr 12

## Combinatorics Seminar

12:20pm - Ford Hall 150
Cyclic Sieving and Cluster Duality for Grassmannian
Linhui Shen, Michigan State
##### Abstract:

The cyclic sieving phenomenon (CSP) was defined by Reiner, Stanton, and White as a generalization of J. Stembridges q=-1 phenomenon. In this talk, we investigate the CSP for plane partitions under a piecewise-linear toggling operation. We place our result in the context of cluster theory for Grassmannians. This is joint work with Daping Weng (Yale University).

Thu Apr 12

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Apr 11

## PDE Seminar

3:35pm - Vincent Hall 570
Asymptotic limit of fractional Allen-Cahn equations and nonlocal minimal surfaces.
Yannick Sire, Johns Hopkins University
##### Abstract:

I will describe recent results on the singular perturbation limit of a fractional Allen-Cahn Equation modeling nonlocal phase transitions. The limiting interface appears to be a stationary nonlocal minimal surface. New nonlocal phenomena appear and the convergence is actually strong, something not happening in the local case. The basic tool is a deep GMT theorem due to Marstrand.

Wed Apr 11

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Apr 11

## Ordway Lecture Series

3:30pm - Vincent Hall 364
Hankel Transforms, Langlands Functoriality and Functional Equation of Automorphic L-functions (II)
Bao Chau Ngo, University of Chicago - Distinguished Ordway Visitor of UMN
Wed Apr 11

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Algebraic Representation Theory Seminar

Tue Apr 10

## Colloquium

3:30pm - Vincent Hall 16
Hankel Transforms, Langlands Functoriality and Functional Equation of Automorphic L-functions (I)
Ordway Visitor - Ngo Bao Chau, University of Chicago
##### Abstract:

Since the beginning of the century, several approaches to Langlands functoriality conjecture have been proposed by Langlands himself, by Braverman-Kazhdan and Lafforgue, ....
In this lecture I will explain how these ideas may be combined and connected to recents works on singularities of certain arc spaces

Tue Apr 10

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Apr 10

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue Apr 10

## Special Events and Seminars

2:30pm - Ford Hall 130

Tue Apr 10

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Human Activity Computing from Inside-out and Outside-in Visual Data
Hyun Soo Park, University of Minnesota, Twin Cities
##### Abstract:

We are witnessing a revolution of artificial intelligence that deeply permeates our lives in aid of large-scale data. However, such AI systems still cannot observe and process underlying mental states such as intent, emotion, and attention while nearly any three-year-old can effortlessly read the meaning of a simple nod, eye contact, or a pointed finger. What makes the three-year-oldand the rest of usso different from these AI systems? My conjecture is the ability to discern microscopic behavioral signals is key, and in this talk, I will present two ways to measure such human activities: leveraging first-person and third-person visual data. Human perception is best captured in first-person videos as naturally following the visual attention of the wearers. This provides a detailed description of physical and social interactions with surrounding objects, people, and scenes. I will show that it is possible to uncover the underlying states that govern the interactions, e.g., control force and joint attention. Human body signals are better measured by third-person videos that convey the global context of the interactions, e.g., spatial relation of objects with face, body, and finger movements. My team has been developing a computational model to reconstruct human activities in 3D at unprecedented resolution by leveraging a large number of third-person videos. To the end, I will argue that these two visual measurements can be complementary, which will produce a powerful tool to analyze human behaviors.

Hyun Soo Park is an Assistant Professor at the Department of Computer Science and Engineering, the University of Minnesota. He is interested in understanding human visual sensorimotor behaviors from visual data. Prior to the UMN, he was a Postdoctoral Fellow in GRASP Lab at University of Pennsylvania. He earned his Ph.D. from Carnegie Mellon University.

Tue Apr 10

## Math Physics Seminar

1:25pm - Vincent Hall 301
Moving frame methods and self-affine fractals
Yun Yang
##### Abstract:

In this talk, we define the notion of affine curvatures on a discrete planar curve. By the moving frame method, they are in fact the discrete Maurer-Cartan invariants. It shows that two curves with the same curvature sequences are affinely equivalent. On the other hand, by using the affine invariants and optimization methods, it becomes possible to collect the IFSs of some self-affine fractals with desired geometrical or topological properties inside a fixed area. In order to estimate their Hausdorff dimensions, GPUs can be used to accelerate parallel computing tasks. Furthermore, the method could be used to a much broader class.

Tue Apr 10

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Apr 10

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Apr 10

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Apr 09

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Applied and Computational Math Colloquium

Mon Apr 09

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Information content of meromorphic continuations of operators
Paul Garrett, University of Minnesota
Mon Apr 09

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Apr 09

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon Apr 09

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri Apr 06

## MCFAM Seminar

4:30pm - Vincent Hall 16
MCFAM Seminar

Fri Apr 06

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Three Problems on expressions of elements of Coxeter groups
Jean-Philippe Labbé, Freie Universität Berlin
##### Abstract:

In 2004, Knutson and Miller asked whether subword complexes of Coxeter groups can be realized as the boundary of simplicial convex polytopes. Subword complexes incarnate several well-known structures: associahedra, finite type cluster complexes, simplices, and even-dimensional cyclic polytopes, for instance. Apart from those, only 1 non-trivial case has been found to be polytopal; this problem requires a deep understanding of reduced expressions in Coxeter groups. In this talk, I will describe three very closely related classical problems on expressions in Coxeter groups that reveal challenging aspects of this open problem.

Fri Apr 06

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Apr 06

## Probability Seminar

2:30pm - Vincent Hall 311
Mutant clone propagation in layered tissue
Katie Storey, UMN
##### Abstract:

Carcinogenesis, the transformation from healthy tissue to invasive cancer, is characterized by the progressive accumulation of mutations in a small group of founder cells. This talk focuses on the spread of premalignant cells during the process of carcinogenesis. We approximate a premalignant clone in layered tissue with a biased voter model on a set of stacked integer lattices. Using the dual process of the biased voter model, we determine the asymptotic propagation speed of the premalignant clone in this setting and compare it to the speed in one layer of tissue, which has been determined previously. Additionally we use this speed within a generalized multi-step model of carcinogenesis, to discuss the clinical implications that arise from differences in the underlying structure of the tissue.

Fri Apr 06

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Apr 06

## MathCEP Seminar

11:15am - Vincent Hall 113
MathCEP Seminar

Thu Apr 05

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Apr 05

## Colloquium

3:30pm - Vincent Hall 16
Boundary Conditions for Crystalline Defects
Ordway Visitor Christoph Ortner, University of Warwick
##### Abstract:

A key problem of atomistic materials modelling is to determine properties of crystalline defects, such as geometries, formation energies, or mobility, from which meso-scopic material properties or coarse-grained models (e.g., diffusion, dislocation dynamics, fracture) can be derived.In this lecture I will focus on the most basic task: determining the equilibrium configuration of a crystalline defect (time permitting I can comment on other properties). Even the very first question, "What is the <exact> model?", warrants discussion. To answer it I will present a thermo-dynamic limit argument which is interesting in its own right but more importantly provides a machinery for quantifying approximation errors in typical computational models, both classical as well as modern multi-scale schemes. It quickly transpires that the error is always due to an approximate descriptions of the crystalline far-field, resulting in an error in the boundary condition. This perspective naturally leads to an exceptionally promising new class of computational schemes where much of the hard work is done analytically in deriving higher-order continuum descriptions of the crystalline far-field.

Thu Apr 05

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Apr 05

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Apr 05

## Student Number Theory Seminar

11:15am - Ford Hall 170
Student Number Theory Seminar

Thu Apr 05

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Apr 04

## PDE Seminar

3:35pm - Vincent Hall 570
The Aviles-Giga functional - A history, a survey and some new results
Andrew Lorent, University of Cincinnati
Wed Apr 04

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Apr 04

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Local cohomology of FI-modules - continuation
Peter Webb, University of Minnesota
##### Abstract:

We complete the discussion of the local cohomology of FI-modules as the homology of a certain complex. This allows a number of deductions, including that the modules are finitely generated, the relationship with depth, bounds on the Nagpal number and regularity.

Tue Apr 03

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Apr 03

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Apr 03

## Topology Seminar

2:30pm - Vincent Hall 2
HF_p is an equivariant Thom spectrum
Dylan Wilson, University of Chicago
##### Abstract:

Mahowald (and later many others) proved that HF_2 is a Thom spectrum for a bundle over the double loop space on the 3-sphere. This has had lots of applications, including (more recently) some nilpotence results for E_2-algebras and a calculation of THH of F_2. In this talk, we explain how to extend the result to the case of equivariant spectra over a cyclic group of prime power order. The case of HF_2 over C_2 is joint with Mark Behrens, and the general case is joint with Jeremy Hahn. If there's time, we'll discuss how this fits into a program of Hill-Hopkins-Ravenel for solving the 3-primary Kervaire invariant problem.

Tue Apr 03

## Special Events and Seminars

2:30pm - Ford Hall 130
Iterative Methods for Computing Square Roots
Meir Jablon
##### Abstract:

We will be discussing Iterative methods for computing square roots. Methods from different historical time periods will be introduced. Also, fixed point algorithms will be discussed at length.

Tue Apr 03

## Math Physics Seminar

1:25pm - Vincent Hall 301
An Observation on the Wigner-von Neumann Potential
Robert W. Numrich, Adjunct Professor of Computer Science City University of New York
##### Abstract:

Roughly speaking, scattering theory is based on the idea that wha goes in comes out. In the quantum mechanical case, this intuitive idea is correct when positive bound states in the continuous spectrum of the hamiltonian operator are avoided. In the classical case, it is correct when capture states in the equations of motion are avoided. For the so-called Wigner-von Neumann potential, a positive bound state exists for the quantum mechanical system and a capture state exists for the classical mechanical system. How are these anomalous states related? Are they more than just a mathematical curiosity?

Tue Apr 03

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Apr 03

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Apr 03

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Apr 02

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Applied and Computational Math Colloquium

Mon Apr 02

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Information content of meromorphic continuation of operators
Paul Garrett
Mon Apr 02

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Apr 02

## Dynamical Systems

2:30pm - Vincent Hall 20
An energy balance model for Arctic sea ice
Kaitlin Hill, University of Minnesota
##### Abstract:

As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation. A challenge in answering this question is that the bifurcation behavior of certain Arctic energy balance models have been shown to be sensitive to how ice-albedo feedback is parameterized. We analyze an Arctic energy balance model in the limit as a smoothing parameter associated with ice-albedo feedback tends to zero, which introduces a discontinuity boundary to the dynamical systems model. Our analysis provides a case study where we use the system in this limit to guide the investigation of bifurcation behavior of the original albedo-smoothed system.

Mon Apr 02

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri Mar 30

## MCFAM Seminar

5:30pm - VinH 16
Quantitative Equity Strategies
2018 Modeling Workshop Team Presentation, U of MN MFM 2018 Modeling Workshop
##### Abstract:

A Student team from the 2018 Financial Mathematics Modeling Workshop will present their work:
Quantitative Equity Strategies; Industry Mentor, Jing Wang
Students in this team utilize an online platform (Quantopian) to implement quantitative equity strategies. Their work centers on the value strategies covered in the book The Guru Investor. Students take the audience through their involvement with fundamental data, programming in Python, back-testing of the quantitative strategies and utilizing a Risk Factor Model to analyze performance attribution

Fri Mar 30

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Coxeter combinatorics of involutions with applications to geometry
Zachary Hamaker, University of Michigan
##### Abstract:

The combinatorics of Coxeter groups has been a rich area of study for many years, motivated by connections to the geometry of flag varieties and representation theory. Building on work of Richardson and Springer, a similar combinatorial theory has been developed for involutions in Coxeter groups. Their original motivation comes from the geometry of spherical varieties. We highlight several aspects of this theory, including the enumeration of reduced words for involutions and a natural characterization of the Chinese monoid. We conclude with some remarks on an apparent relationship between type A spherical varieties and the geometry of the orthogonal and Lagrangian Grassmannians. This is joint work with Brendan Pawlowski and Eric Marberg.

Fri Mar 30

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Mar 30

## Probability Seminar

2:30pm - Vincent Hall 311
Level sets of random functions in high dimensions: a thermodynamic approach.
Antonio Auffinger, Northwestern University
##### Abstract:

What does a random Morse function look like on a high-dimensional sphere? How many critical values of given index, or below a given level? What can be said about the topology of its level sets? In this talk, we will address these questions by looking at the low temperature limit of the corresponding Gibbs measure. In particular, we will provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass. These examples largely contrast with the early prediction that random functions could be classified into two different categories: one-step replica symmetry breaking (1RSB) or full-step replica symmetry breaking (FRSB). Based on a joint work with Qiang Zeng (Northwestern).

Fri Mar 30

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Mar 30 11:15am - Vincent Hall 113
MathCEP Seminar

Thu Mar 29

## Special Events and Seminars

4:45pm - Vincent Hall 364
On certain special values of L-functions associated to elliptic curves and real quadratic fields
Chung Pang Mok, Purdue University
##### Abstract:

We study certain normalized special values of L-functions associated to elliptic curves and real quadratic fields. Under certain hypothesis, we are able to show that these are squares of rational numbers. This result can be regarded as instances of the rank zero case of the Birch and Swinnerton-dyer conjecture modulo squares, and is related to a theorem of Bertolini-Darmon on rationality of Stark-Heegner points over genus fields of real quadratic fields.

Thu Mar 29

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Mar 29

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Thu Mar 29

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Mar 29

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Mar 29

## Student Number Theory Seminar

11:15am - Ford Hall 170
Student Number Theory Seminar

Thu Mar 29

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Mar 28

## PDE Seminar

3:35pm - Vincent Hall 570
The oblique derivative problem in Lipschitz domains
Hongjie Dong, Brown University
##### Abstract:

I will present a recent work about the W^2_p estimate for the oblique derivative problem for nondivergence form elliptic equations with VMO coefficients in Lipschitz domains with locally small Lipschitz constant. This improves an earlier result by G. Lieberman, where the domains are required to be in C^{1,a} for a > 1-1/p. An extension to fully nonlinear equations will also be discussed. Joint work with Zongyuan Li (Brown).

Wed Mar 28

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Mar 28

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Local cohomology of FI-modules
Peter Webb, University of Minnesota
##### Abstract:

We define the local cohomology of FI-modules and show that it is computed as the homology of a certain complex. This allows a number of deductions, including that the modules are finitely generated, and the relationship with depth.

Tue Mar 27

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 27

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Mar 27

## Topology Seminar

2:30pm - Vincent Hall 2
Topological Hochschild Homology and Characteristics
Jonathan Campbell, Vanderbilt University
##### Abstract:

In this talk I'll review the definition of duality in categories and bicategories and how certain functors called "shadows", due to Kate Ponto, can be used to extract Euler characteristic-type invariants from this data. It turns out that topological Hochschild homology (which I'll define) is an example of such a shadow, and this can be used to relate classical invariants from fixed point theory (e.g. the Reidemeister trace) with the image of the cyclotomic trace in K-theory. Time permitting, I'll sketch how anything that one calls a "characteristic" should fit into this story. This is joint work with Kate Ponto.

Tue Mar 27

## Special Events and Seminars

2:30pm - Ford Hall 130
The Poisson Process and Phylogenetic Trees
Mansi Bezbaruah
##### Abstract:

A phylogenetic tree is a visual representation of the relationship between different organisms, showing the path through evolutionary time from a common ancestor to different descendants. It is hypothesized that the growth of uniform pure-birth Phylogenetic Trees can be simulated by a Poisson growth. This project is an exploration into the expectations of a Poisson-directed growth of Phylogenetic Trees.

Tue Mar 27

## IMA Data Science Lab Seminar

1:25pm - MCB 2-120
Primal-Dual Optimization Algorithms Over Riemannian Manifolds: An Iteration Complexity Analysise
Junyu Zhang, University of Minnesota, Twin Cities
##### Abstract:

We study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing, image processing, and tensor PCA, among others. We develop an ADMM-like primal-dual approach based on decoupled solvable subroutines such as linearized proximal mappings. First, we introduce the optimality conditions for the afore-mentioned optimization models. Then, the notion of $\epsilon$-stationary solutions is introduced as a result. The main part of the paper is to show that the proposed algorithms enjoy an iteration complexity of $O(1/\epsilon^2)$ to reach an $\epsilon$-stationary solution. For prohibitively large-size tensor or machine learning models, we present a sampling-based stochastic algorithm with the same iteration complexity bound in expectation. In case the subproblems are not analytically solvable, a feasible curvilinear line-search variant of the algorithm based on retraction operators is proposed. Finally, we show specifically how the algorithms can be implemented to solve a variety of practical problems such as the NP-hard maximum bisection problem, the $\ell_q$ regularized sparse tensor principal component analysis and the community detection problem. Our preliminary numerical results show great potentials of the proposed methods.

Junyu Zhang is a third year PhD student in the Industrial and System Engineering Department of the University of Minnesota. His research interests are mainly in designing and analyzing complexity for the convex and nonconvex continuous optimization, Riemannian optimization and stochastic optimization algorithms.

Tue Mar 27

## Math Physics Seminar

1:25pm - Vincent Hall 301
Dispersive Lamb Systems
Natalie Sheils
##### Abstract:

Under periodic boundary conditions, a one-dimensional dispersive medium driven by a Lamb oscillator exhibits a smooth response when the dispersion relation is asymptotically linear or superlinear at large wave numbers, but unusual fractal solution profile emerge when the dispersion relation is asymptotically sublinear. Strikingly, this is exactly the opposite of the superlinear asymptotic regime required for fractalization and dispersive quantization, also known as the Talbot effect, of the unforced medium induced by discontinuous initial conditions.

Tue Mar 27

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Mar 27

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Mar 27

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Mar 26

## Differential Geometry and Symplectic Topology Seminar

4:30pm - Vincent Hall 570
Isometric embedding via strongly symmetric positive systems
##### Abstract:

(Joint work with Gui-Qiang Chen, Marshall Slemrod, Dehua Wang, and Deane Yang)

In this talk, I will give an outline of our new proof for the local existence of a smooth isometric embedding of a smooth 3-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into 6-dimensional Euclidean space. Our proof avoids the sophisticated microlocal analysis used in earlier proofs by Bryant-Griffiths-Yang and Nakamura-Maeda; instead, it is based on a new local existence theorem for a class of nonlinear, first-order PDE systems that we call "strongly symmetric positive." These are a subclass of the class of symmetric positive systems, which were introduced by Friedrichs in order to study certain PDE systems that do not fall under one of the standard types (elliptic, hyperbolic, and parabolic).

As in earlier proofs, we construct solutions via the Nash-Moser implicit function theorem, which requires showing that the linearization of the isometric embedding PDE system near an approximate embedding has a smooth solution that satisfies "smooth tame estimates." We accomplish this in two steps:
(1) Show that the approximate embedding can be chosen so that the reduced linearized system becomes strongly symmetric positive after a carefully chosen change of variables.
(2) Show that any such system has local solutions that satisfy smooth tame estimates.

The main advantage of our approach is that step (2) is much more straightforward than similar results for other classes of PDE systems used in prior proofs, while step (1) requires only linear algebra.

The talk will focus on the main ideas of the proof; technical details will be kept to a minimum.

Mon Mar 26

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Stochastic averaging for multiple scale models driven by fat-tailed noise
Rachel Kuske, Georgia Tech and University of British Columbia
##### Abstract:

Stochastic averaging has a long history for systems with multiple time scales and Gaussian forcing, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as in Levy processes or alpha-stable noise. Correlated additive and multiplicative (CAM) Gaussian noise, with infinite variance or fat tails in certain parameter regimes, can arise generically in many models with parametric uncertainty and has received increased attention in the context of atmosphere and ocean dynamics. These applications motivate new reduced models using stochastic averaging for systems with fast processes driven by noise with fat tails. We develop these results for the case of alpha-stable noise, giving explicit results that use the Marcus interpretation, the infinite variance analog to the Stratonovich interpretation. Then we show how reduced models for systems driven by fast linear CAM noise processes can be connected with the stochastic averaging for multiple scales systems driven by alpha-stable processes. We identify the conditions under which the approximation of a CAM noise process is valid in the averaged system, and illustrate methods using effectively equivalent fast, infinite-variance processes. These new types of approximations open the door for stochastic averaging in a wider range of stochastic systems with multiple time scales.

This is joint work with Prof. Adam Monahan (U Victoria) and Dr. Will Thompson (UBC/NMi Metrology and Gaming)

Mon Mar 26

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Curiosities of exotic eigenfunction expansions, continued
Mon Mar 26

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Mar 26

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon Mar 26

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri Mar 23

## MCFAM Seminar

5:30pm - Vincent Hall 16
Where Less Is More: Reducing Variable Annuity Fees to Benefit Policyholder and Insurer
Thorsten Moenig, Temple University
##### Abstract:

In the United States, variable annuities (VAs) are popular long-term personal investment vehicles. Recently, however, sales have begun to dwindle. In fact, financial advisers have long argued against investing in VAs due to the products' high fees. VA providers charge these fees---typically at a constant rate throughout the policy period---to cover their expenses and the costs of embedded guarantees, and lowering this constant fee rate could make the VA unprofitable. Instead, we propose and analyze a simple change to the fee structure that would lower fee rates overall (and thus make the product more attractive to investors) without reducing the insurer's profit. The key insight is that this time-dependent fee rate (with moderate front-loading) implicitly discourages policy lapses and exchanges, which reduces the providers' policy acquisition expenses. Taking into account financially optimal lapse (and reentry) decisions, we determine the optimal timing and rate of the fee reduction for a competitive as well as for an innovative VA provider. An important characteristic of this feature is that it can be implemented easily and effectively to both new and existing VA policies.

Fri Mar 23

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Sandpiles and representation theory
Vic Reiner
##### Abstract:

Every graph has a subtle invariant, called its sandpile group: a finite abelian group whose size is the number of spanning trees in the graph. After reviewing this, we will discuss an analogous "sandpile group" for any representation of a finite group, motivated in part by the classical McKay correspondence.
(Based on joint work with Georgia Benkart, Carly Klivans, Christian Gaetz, Jia Huang, and Darij Grinberg.)

Fri Mar 23

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Mar 23

## Probability Seminar

2:30pm - Vincent Hall 311
Talagrand Concentration Inequalities for Stochastic Partial Differential Equations
Andrey Sarantsev, University of California, Santa Barbara
##### Abstract:

For a heat-type stochastic partial differential equation (SPDE), we prove Talagrand concentration of measure inequality, which compares Wasserstein distance between the distribution of the solution and a test probability measure with relative entropy of this test measure with respect to this distribution. This implies Gaussian-type bounds on any Lipschitz function of the solution. This continues similar work of Soumik Pal for stochastic ordinary differential equations. Joint work with Davar Khoshnevisan.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.0px; font: 13.0px Arial; color: #232323; -webkit-text-stroke: #232323}span.s1 {font-kerning: none}

Fri Mar 23

## Analysis and PDE Working Seminar

2:30pm - Vincent Hall 207
The Effects of Diffusion and Spatial Heterogeneity in Total Population and Carrying Capacity
Chieh-Hsin Lai
Fri Mar 23

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Use of Quantitative Methods to Support Keytruda Dose Selection
Anna Kondic, Merck & Co, Inc.
##### Abstract:

Anna Georgieva Kondic
PhD MBADistinguished Scientist, Economic and Data Sciences
Merck Pharmaceuticals

Recently, immunotherapy has yielded promising results in several cancer types. Contrary to the established classical chemotherapy-dosing paradigm, a maximum tolerated dose approach does not always produce better clinical outcomes for novel targeted therapies, as their efficacy is frequently robust at pharmacologically active doses below the maximum tolerated dose. Integrated safety and efficacy assessments are needed to inform clinical dose and trial design, and to support an early identification of potentially safe and efficacious combination treatments. In this talk, I will walk you through the history of how the dose for Mercks immunomodulatory drug pembrolizumab (Keytruda) was selected; how the transition from weight-based to fixed dose was made and how mathematical modeling and data science is helping shape the field of drug development.

Anna Georgieva Kondic is a mathematician by training, receiving her PhD in Mathematical Physics from Duke University in 1998. Anna holds a degree in Business Administration from NYU, with a specialization in negotiations.

Anna is currently a distinguished scientist in the Data and Economic Sciences department at Merck and Co, where she is responsible for the implementation of economic models in the early space of R&D. Prior to her current position, Anna was part of Mercks quantitative pharmacology department, where she was responsible (among other things) for the filing strategy and clinical pharmacology dossier for Mercks immunomodulatory drug Keytruda, currently approved for multiple tumor types.
Before Merck, Anna spent 11 years at Novartis, where she supported arthritis, osteoporosis, Oncology, diabetes and cardio-vascular disease using both empirical and mechanistic models to aid quantitative decision making.

Fri Mar 23

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Mar 23

## MathCEP Seminar

11:15am - Vincent Hall 113
Collaborative problem-based learning in mathematics: A cognitive load perspective
Kaitlin Hill, University of Minnesota
##### Abstract:

Mathematics educators have struggled to improve learners performance in mathematics. Based on the cognitive load theory, many conventional instructional formats are less than effective because little consideration is given to the concept of cognitive processing capacity. Thus, investigation into problem-based learning (PBL) has been undertaken. This study examined the effects of PBL on educational statistics course. Six PBL modules, which consisted of scenarios and guided questions, were used during a 10-week teaching. Comparing students performances based on two tests showed that there was a significant difference between the mean performance of the PBL group and that of the conventional group  indicating PBL efficacy.

Thu Mar 22

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Mar 22

## Colloquium

3:30pm - Vincent Hall 16
Statistics of the Riemann Zeta Function and L-functions
Michael Rubinstein, University of Waterloo
##### Abstract:

The Riemann Zeta function and related L-functions stand
at the epicenter of number theory. They have played a crucial role in
our understanding of fundamental arithmetic and algebraic objects. But
many basic questions about their properties elude us. In my talk l
will give an overview of various fascinating statistics, some proven
and others conjectural, concerning the Riemann Zeta function and
L-functions.

Thu Mar 22

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Mar 22

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Mar 22

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Mar 21

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Mar 21

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Mar 21

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Injective FI-modules, part 2
Peter Webb, University of Minnesota
##### Abstract:

Over a field of characteristic zero a theorem of Sam and Snowden characterizes finitely generated injective FI-modules. Over a field of characteristic p the category of FI-modules does not have enough injectives.

Tue Mar 20

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 20

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Mar 20

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue Mar 20

## Special Events and Seminars

2:30pm - Ford Hall 130
How Quick is a Cookie Random Walk?
Owen Levin
##### Abstract:

Cookie Random Walks are a discrete model for self-interacting random motion. At each time step, the transition probabilities to the next site depend on how many times the walker has visited its current location. In this talk, we will explore the limiting speed of such walks, which is a fancy way of saying the average ratio of the distance from the origin versus the time it took to get there. The goal of this talk is to give intuition for how one might try to analyze this speed starting from basic principles. I will try to assume little to no previous experience with the topics discussed.

Tue Mar 20

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Accelerated Gradient PDE's: The active contour case
Anthony Yezzi, Georgia Institute of Technology
##### Abstract:

Following the seminal work of Nesterov, accelerated optimization methods (sometimes referred to as momentum methods) have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios were second-order optimization strategies are either inapplicable or impractical. Not only does accelerated gradient descent converge considerably faster than traditional gradient descent, but it performs a more robust local search of the parameter space by initially overshooting and then oscillating back as it settles into a final configuration, thereby selecting only local minimizers with a attraction basin large enough to accommodate the initial overshoot. This behavior has made accelerated search methods particularly popular within the machine learning community where stochastic variants have been proposed as well. So far, however, accelerated optimization methods have been applied to searches over finite parameter spaces. We show how a variational framework for these finite dimensional methods (recently formulated by Wibisono, Wilson, and Jordan) can be extended to the infinite dimensional setting and, in particular, to the manifold of planar curves in order to yield a new class of accelerated geometric, PDE-based active contours.

Tue Mar 20

## Math Physics Seminar

1:25pm - Lind Hall 305
Cross-listed Data Science Talk - Accelerated Gradient PDE's: The active contour case
Anthony Yezzi, Georgia Institute of Technology
##### Abstract:

Following the seminal work of Nesterov, accelerated optimization methods (sometimes referred to as momentum methods) have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios were second-order optimization strategies are either inapplicable or impractical. Not only does accelerated gradient descent converge considerably faster than traditional gradient descent, but it performs a more robust local search of the parameter space by initially overshooting and then oscillating back as it settles into a final configuration, thereby selecting only local minimizers with a attraction basin large enough to accommodate the initial overshoot. This behavior has made accelerated search methods particularly popular within the machine learning community where stochastic variants have been proposed as well. So far, however, accelerated optimization methods have been applied to searches over finite parameter spaces. We show how a variational framework for these finite dimensional methods (recently formulated by Wibisono, Wilson, and Jordan) can be extended to the infinite dimensional setting and, in particular, to the manifold of planar curves in order to yield a new class of accelerated geometric, PDE-based active contours.

Tue Mar 20

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Mar 20

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Mar 20

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Mar 19

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Applied and Computational Math Colloquium

Mon Mar 19

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Some curiosities of exotic eigenfunction expansions
Mon Mar 19

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Mar 19

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon Mar 19

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri Mar 16

## MCFAM Seminar

4:30pm - Vincent Hall 16
MCFAM Seminar

Fri Mar 16

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar - No Seminar

Fri Mar 16

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Mar 16

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Mar 16

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Mar 16 11:15am - Vincent Hall 113
MathCEP Seminar

Thu Mar 15

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Mar 15

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Thu Mar 15

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Mar 15

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Mar 15

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Mar 14

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Mar 14

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Mar 14

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Algebraic Representation Theory Seminar

Tue Mar 13

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 13

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Mar 13

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue Mar 13

## Special Events and Seminars

2:30pm - Ford Hall 130

Tue Mar 13

## Math Physics Seminar

1:25pm - Vincent Hall 301
Math Physics Seminar

Tue Mar 13

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Mar 13

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Mar 13

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Mar 12

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Applied and Computational Math Colloquium

Mon Mar 12

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Forms and Number Theory

Mon Mar 12

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Mar 12

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon Mar 12

## Topology Seminar

1:30pm - Vincent Hall 209
Topology Seminar

Fri Mar 09

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Mar 09

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Ice and Everything Else
Benjamin Brubaker
##### Abstract:

We'll discuss how solvable lattice models (including the "square ice" model of the title) sit at the nexus of so many interesting fields of mathematics, including combinatorics, mathematical physics, representation theory, and algebraic topology, to name a few. Examples will include both the Jones polynomial for distinguishing knots and Kuperberg's proof of the alternating sign matrix conjecture.  Yet other examples we'll mention are joint work with Bump and Friedberg, and a more recent paper with Schultz.

Fri Mar 09

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Mar 09

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Mar 09

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Industrial Analytics  a Balanced Approach
Girija Parthasarathy, Honeywell
##### Abstract:

Often, applying data science and analytics in the industrial IoT space is considered an extension of general big data tools and data science approaches. However, industrial machinery data have unique attributes, challenges and opportunities for insights and value creation. Simply trying to fit the industrial analytics peg into the big data square hole creates complications  from exploration to feasibility to production. In this talk, I will outline the technological forces that are driving software and data transformations in traditionally industrial companies; what differentiates industrial big data from general big data; provide examples of analytics development practices that have been effective, and the importance of a balanced approach.

Bio:
Dr. Girija Parthasarathy is Analytics lead and Senior Customer Engagement Manager at Honeywell Aerospace. She is an experienced technologist and program manager and has managed global multi-disciplinary teams running data science and R&D programs in different Honeywell divisions. She is experienced in identifying new technology opportunities, seeding, maturing and delivering them through technology transfer into business units. Her technical expertise includes data analytics combining data driven and physics based modeling, in the domains of aircraft systems, wind turbines, building energy efficiency and smart grid; and computational modeling in the areas of combustion, emissions, and heat transfer. Girija holds several patents, and has authored several peer-reviewed journal and conference papers and has been an invited speaker at different venues. Girija earned a BS in Energy engineering from the Indian Institute of Technology and a PhD in Mechanical Engineering from the University of Minnesota.

Fri Mar 09

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Mar 09 11:15am - Vincent Hall 113
MathCEP Seminar

Thu Mar 08

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Mar 08

## Colloquium

3:30pm - Vincent Hall 16
SRB measures for infinite-dimensional dynamical systems with potential applications to PDE
Alex Blumenthal, University of Maryland
##### Abstract:

I will talk about the extension to the setting of Banach space mappings a concept which has proven highly useful in the study of finite-dimensional dynamical systems exhibiting chaotic behavior, that of SRB measures. This extended notion of SRB measure and our results potentially apply to a large class of dissipative PDE, including dissipative parabolic and dispersive wave equations.

We generalize two results known in the finite-dimensional setting. The first is a geometric result, absolute continuity of the stable foliation, which in particular implies that an SRB measure with no zero exponents is visible, in the sense of time averages converging to spatial averages, with respect to a large subset of phase space. The second is the characterization of the SRB property in terms of the relationship between a priori different quantifications of chaotic behavior, Lyapunov exponents and metric entropy.

Complications of our infinite-dimensional environment include: (1) the absence of Lebesgue measure as a reference measure, not even k-dimensional volume elements (whereas the finite dimensional theory heavily involves the notion of volume growth along unstable leaves); and (2) mappings in our setting are not locally onto or differentiably invertible, possibly exhibit arbitrarily strong rates of contraction (even near attractors).

This work is joint with Lai-Sang Young.

Thu Mar 08

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Stable equivalence of smoothly knotted surfaces
Dave Auckly, Kansas State University
##### Abstract:

t is well known that there are smoothly inequivalent, objects in 4-dimensions that are topologically equivalent. Fairly general results exist stating that such objects become smoothly equivalent after some number of stabilizations. Until this past summer the only thing known about the number of stabilizations needed was an infinite collection of examples where one stabilization was enough.

This talk will present the proof of a theorem demonstrating that when the easiest topological invariants are trivial two smooth surfaces become smoothly isotopic after just one stabilization.
This is joint work with Kim, Melvin, Ruberman and Schwartz.

We will also present joint work with Ruberman aimed at the difference between the homotopy groups of the diffeomorphism group and the homotopy groups of the homeomorphism group.

Thu Mar 08

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Mar 08

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Mar 07

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Mar 07

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Mar 07

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Injective FI-modules
Peter Webb, University of Minnesota
##### Abstract:

We show that torsion FI-modules and #-filtered modules are orthogonal with respect to Ext. We characterize the finitely generated injective modules in characteristic zero.

Tue Mar 06

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Mar 06

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Mar 06

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue Mar 06

## Special Events and Seminars

2:30pm - Ford Hall 130
Grammar Induction: Unsupervised Learning for Natural Language - Canceled
Eishani Kumar
##### Abstract:

Language parsers are traditionally are built around a large corpora of marked up text. While they can be generated semi-automatically, treebanks for natural language still must be manually reviewed and thus requires large amounts of time and expertise to create. Grammar induction attempts to find the hierarchical structure of a given language in a unsupervised manner, eliminating the need of this expensive labor. Here we discuss the current research involved in grammar induction, its limitations, and multilingual applications for this technology.

Tue Mar 06

## Math Physics Seminar

1:25pm - Vincent Hall 301
Singularities of non-commutative integrable systems
Rui Loja Fernandes, University of Illinois at Urbana-Champaign
##### Abstract:

For classical finite dimensional integrable systems there is a well developed theory of singularities. In this talk I will talk about the first steps in a theory for singularities of non-commutative integrable systems (not to be confused with quantum integrable systems!).

Tue Mar 06

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Mar 06

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Mar 06

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Mar 05

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Transport and Feedback in Models of Self­ Organizing Vegetation Patterns in Dryland Ecosystems
Mary Silber, University of Chicago
##### Abstract:

Bands of vegetation alternating periodically with bare soil have been observed in many dryland environments since their discovery in the Horn of Africa in the 1950s. Mathematical modeling efforts over the past two decades have sought to account for these bands via a self­ organizing interaction between vegetation and water resources. Understanding the processes underlying vegetation patterns in arid and semi­ arid regions is important to predict desertification risk under increasing anthropogenic pressure. Various modeling frameworks have been proposed that are capable of generating similar patterns through self­ organizing mechanisms which stem from key assumptions regarding plant feedbacks on surface/subsurface water transport. We discuss a hierarchy of hydrology­/vegetation models for the coupled dynamics of surface water, soil moisture, and vegetation biomass on a hillslope. We identify distinguishing features and trends for the periodic traveling wave solutions when there is an imposed idealized topography and make some comparisons to satellite images of large ­scale banded vegetation patterns in drylands of Africa, Australia and North America.

Mon Mar 05

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Forms and Number Theory - Postponed

Mon Mar 05

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Mar 05

## Topology Seminar

2:30pm - Vincent Hall 209
Topology Seminar

Mon Mar 05

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon Mar 05

## Dynamical Systems

2:30pm - Vincent Hall 20
Traveling waves and patterns in multiple timescale reaction diffusion equations
Paul Carter, University Leiden
##### Abstract:

Reaction diffusion PDEs are prototypical models in the study of pattern forming processes. Within these models, many such patterns arise in the form of traveling waves, which are profiles with fixed shape that move with constant speed. In this talk, I will discuss the formation of traveling waves in systems with timescale separation, in which the dynamics separate into slow and fast components. I will focus primarily on the construction of traveling wave solutions in two applications: vegetation stripe pattern formation in semiarid regions, described by the Klausmeier equation, and a transition from single to double pulses occurring in the FitzHugh--Nagumo system, a simplified model of nerve impulse propagation. The existence proofs capitalize on the slow/fast geometry of the associated traveling wave ODEs and the techniques of geometric singular perturbation theory, Lin's method, and blow-up desingularization.

Fri Mar 02

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Mar 02

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Double jump phase transition in a random soliton cellular automaton
Hanbaek Lyu, Ohio State
##### Abstract:

n this talk, we consider the soliton cellular automaton introduced by Takahashi and Satsuma in 1990 with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first $n$ boxes are occupied independently with probability $p\in(0,1)$, then the number of solitons is of order $n$ for all $p$, and the length of the longest soliton is of order $\log n$ for $p1/2$, order $\sqrt{n}$ for $p=1/2$, and order $n$ for $p>1/2$. Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed $j\geq 1$, the top $j$ soliton lengths have the same order as the longest for $p\leq 1/2$, whereas all but the longest have order at most $\log n$ for $p>1/2$. As an application, we obtain scaling limits for the lengths of the $k^{\text{th}}$ longest increasing and decreasing subsequences in a random stack-sortable permutation of length $n$ in terms of random walks and Brownian excursions.

This is a joint work with Lionel Levine and John Pike.

Fri Mar 02

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Mar 02

## Probability Seminar

2:30pm - Vincent Hall 311
Pursuit Games and Shy Couplings
Maury Bramson, UMN
##### Abstract:

This will be the continuation of previous week's talk.

Fri Mar 02

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Mar 02 11:15am - Vincent Hall 113
MathCEP Seminar

Thu Mar 01

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Mar 01

## Colloquium

3:30pm - Vincent Hall 16
Associativity and Integrability
Ordway Visitor - Rui Loja Fernandes, University of Illinois at Urbana-Champaign
##### Abstract:

A fundamental result of Lie theory is Lies Third Theorem which states that every finite dimensional Lie algebra integrates to a Lie group. This result fails for infinite dimensional Lie algebras (e.g., Banach Lie algebras) and it also fails for (finite dimensional) Lie algebroids. But every reasonable Lie algebra (finite or infinite dimensional) integrates to a local Lie group and every Lie algebroid integrates to a local Lie groupoid. On the other hand, a classical theorem of Malcev states that a local group is enlargeable to a group if and only if it is global associative. This talk will be an introduction to Lie algebroids and groupoids, focusing on the failure of Lies Third Theorem and its relationship to the failure of associativity.

Thu Mar 01

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Topology of Enumerative Problems: Inflection Points on Cubic Curves
Weiyan Chen, University of Minnesota
Thu Mar 01

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Mar 01

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Feb 28

## PDE Seminar

3:35pm - Vincent Hall 570
Uniform Rectifiability and Elliptic Partial Differential Equations
Simon Bortz, University of Minnesota
##### Abstract:

In geometric measure theory, the notion of rectifiability plays a central role. Roughly speaking, a set is rectifiable if and only if it possesses "measure theoretic tangents". Around 1990, Guy David and Stephen Semmes introduced a quantitative notion of rectifiability, uniform rectifiability. This turns out to be the appropriate rough setting for several standard' harmonic analysis tools to work (L^2 boundedness of singular integrals, Littlewood-Paley, etc.). Recently, there has been a significant interest in providing (elliptic) PDE characterizations of uniformly rectifiable sets. Several such characterizations have been furnished by combining the work of Hofmann-Martell-Mayboroda ('14) and Azzam-Garnett-Mourgoglou-Tolsa ('16). I will survey these results and report on some of my own work in this area, which characterizes uniform rectifiability of a set by control on the oscillation of bounded harmonic functions on the complement of the set.

Wed Feb 28

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Feb 28

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Adjoints of the shift functor for FI-modules and acyclicity of #-filtered modules
Peter Webb, University of Minnesota
##### Abstract:

I will conclude the properties of the adjoint functors of the shift functor following Ramos and Li, and start on some consequences.

Tue Feb 27

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Feb 27

## Colloquium

2:30pm - Vincent Hall 16
Colloquium

Tue Feb 27

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue Feb 27

## Special Events and Seminars

2:30pm - Ford Hall 130

Tue Feb 27

## Math Physics Seminar

1:25pm - Vincent Hall 301
Archaeological Site Reconstruction at Dmanisi, Georgia: Using Modern Geometric Methods and Machine Learning to Classify and Refit Fragmented Faunal Remains
Katrina Yezzi-Woodley, Department of Anthropology
##### Abstract:

Modern geometric methods and machine learning could revolutionize zooarchaeology. Archaeological sites are filled with thousands of bone fragments. Accurately identifying these remains and the agents responsible for modifying them is essential to site formation reconstruction and the identification of human activity. Here I introduce new methods that use powerful, advanced mathematics and technology to classify bone fragments according to the agents that broke them and to develop a method for automatic refits to increase the number of identifiable specimens. These experimentally derived methods will be applied to fragments from the Pleistocene site of Dmanisi, Georgia (Transcaucasia) (~1.78 Ma) to reconstruct site formation processes there.

Tue Feb 27

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Feb 27

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Feb 27

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Feb 26

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Producing divergence free approximations to incompressible flows
Johnny Guzman, Brown University
##### Abstract:

Finite element methods are widely used in approximating incompressible flows. However, most methods produce discrete velocity fields that are NOT divergence free although this property is desirable. In this talk, we discuss the obstacles in producing stable and divergence free producing numerical methods. We then show several examples of methods that achieve this. This is joint work with Michael Neilan and Ridgway Scott.

Mon Feb 26

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Moderate-growth automorphic forms and rapid-decay automorphic distributions
Joe Dickinson, University of Minnesota
Mon Feb 26

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Feb 26

## Topology Seminar

2:30pm - Vincent Hall 209
Topology Seminar

Mon Feb 26

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dnamical Systems Seminar

Mon Feb 26

## Math Biology Seminar

1:30pm - Vincent Hall 313
Linking the micro- and macro-scales in populations of swimming cells
Eric Keaveny, Imperial College
##### Abstract:

Swimming cells and microorganisms are as diverse in their collective dynamics as they are in their individual shapes and swimming mechanisms. They are able to propel themselves through simple viscous fluids, as well as through more complex environments where they must interact with other microscopic structures. In this talk, I will describe recent simulations that explore the connection between dynamics at the scale of the cell with that of the population in the case where the cells are sperm. In particular, I will discuss how the motion of the sperms flagella can greatly impact the overall dynamics of their suspensions. Additionally, I will discuss how in complex environments, the density and stiffness of structures with which the cells interact impact the effective diffusion of the population.

Fri Feb 23

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Feb 23

## MCFAM Seminar

5:30pm - Vincent Hall 16
Modeling and Coding Work of a Quantitative Risk Analyst and MFM Alumna
##### Abstract:

As an alumna of the MFM program within MCFAM I learned many things that I have used in my current role as a quantitative risk analyst. In this presentation I will cover the overall elements of good quantitative risk analysis as well as two examples that demonstrate how I use the knowledge I gained from the program.

Bio: Samantha is a Quant Risk Analyst who has been working at Geneva Trading in Chicago since 2015. Her colleagues in the Risk Analysis Department at Geneva describe her as "their quant". She has worked on a variety of projects to assist implementation of risk models, analyze risk metrics and monitor risk on a real time basis. Prior to Geneva Samantha was a Quantitative Risk Analyst Consultant at the CME Group and a Systems Analyst at Options Clearing Corporation (OCC). She received her MFM from the University of Minnesota in 2013 and her Bachelor's Degree in Econometrics from Shanghai University of Finance and Economics in 2011.

Fri Feb 23

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Biclosed sets in representation theory
Alexander Garver, UQAM
##### Abstract:

The weak order on elements of a Coxeter group appears in many mathematical contexts including geometric combinatorics, generalized associahedra, and representation theory of preprojective algebras. The weak order may be equivalently described using biclosed sets. We study lattices of biclosed sets that generalize the weak order on permutations. We show that any such lattice of biclosed sets is isomorphic to subcategories of the module category of an analogue of the preprojective algebra, which we call torsion shadows. If time permits, we will present a similar description of the shard intersection order of these lattices of biclosed sets. This is joint work with Thomas McConville and Kaveh Mousavand.

Fri Feb 23

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Feb 23

## Analysis and PDE Working Seminar

3:00pm - Vincent Hall 207
Functional Analytic Approaches to Self-improvement Properties for Local and Non-local Differential Equations

Fri Feb 23

## Probability Seminar

2:30pm - Vincent Hall 311
Pursuit Games and Shy Couplings
Maury Bramson, UMN
##### Abstract:

We are interested in the question of when a shy coupling, for a pair of Brownian motions, exists in a given bounded domain. That is, is it possible to construct a (non-anticipating) coupling between a pair of Brownian motions so that, with positive probability, they are always at least some assigned distance apart? This question is related to the deterministic Lion and Man problem, with the Lion attempting to capture the Man when both are allowed to move at the same rate. This talk is based on joint work with K. Burdzy and W. Kendall.

Fri Feb 23

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Guy-vanie Miakonkana, Travelers Insurance
Fri Feb 23

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Feb 23

## MathCEP Seminar

11:15am - Vincent Hall 113
Video Textbooks In The Active Learning Classroom
Mike Weimerskirch
##### Abstract:

As our computational power increases with each new technological advance, our need for proficiency in higher-order thinking skills grows. That is the thought behind the flipped classroom, which enables instructors to focus on deeper thought processes during class time, while relegating routine tasks to readings, videos and practice that students do outside of the classroom. The standard approach is to record video lectures based on a printed text. A better approach is to begin the instruction with the video as the primary source of imparting information to students. Video offers a greater flexibility in presenting concepts and connecting ideas. The University of Minnesota now uses open source video textbooks to teach its pre-calculus courses in active learning classrooms.

Thu Feb 22

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Feb 22

## Colloquium

3:30pm - Vincent Hall 16
Front capturing schemes for nonlinear PDEs with a free boundary limit
Li Wang, State University of New York at Buffalo
##### Abstract:

Evolution in physical or biological systems often involves interplay between nonlinear interaction among the constituent particles, and convective or diffusive transport, which is driven by density dependent pressure. When the pressure-density relationship becomes highly nonlinear, the evolution equation converges to a free boundary problem as a stiff limit. In terms of numerics, the nonlinearity and degeneracy bring great challenges, and there is lack of standard mechanism to capture the propagation of the front in the limit. In this talk, I will introduce a numerical scheme for tumor growth models based on a prediction-correction reformulation, which naturally connects to the free boundary problem in the discrete sense. As an alternative, I will present a variational method for a class of continuity equations (such as the Keller-Segel model) using the gradient flow structure, which has built-in stability, positivity preservation and energy decreasing property, and serves as a good candidate for capturing the stiff pressure limit.

Thu Feb 22

## Differential Geometry and Symplectic Topology Seminar

1:30pm - Vincent Hall 570
On Symplectic Fillings and Milnor Fibers of Quotient Surface Singularities
Professor Jongil Park, Seoul National University
##### Abstract:

Abstract
One of active research areas in symplectic 4-manifolds is to cassify symplectic fillings of certain 3-manifolds equipped with a contact structure. Among them, people have long studied symplectic fillings of the link of a quotient surface singularity. Note that the link of a quotient surface singularity carries a canonical contact structure which is also known as the Milnor fillable contact structure. One the other hand, algebraic geometers also have studied Milnor fibers as a general fiber of
smoothings for a quotient surface singularity.
In this series of talks, Id like to review basics on symplectic fillings and Milnor fibers of quotient surface singularities. Then I will explain some recent works on symplectic fillings and Milnor fibers of quotient surface singularities. The 1st talk is a review of known results on symplectic fillings and Milnor fibers of quotient surface singularities, and the 2nd talk is about identifying minimal symplectic fillings with Milnor fibers of quotient surface singularities (joint work with Heesang
Park, Dongsoo Shin and Giancarlo Urz´ua). In the 3rd talk, Ill also explain how we interpret minimal symplectic fillings of quotient surface singularities as positive allowable Lefschetz fibrations (joint work with Hakho Choi). A tentative schedule is the following:
Talk 1: 2/8(Thur) A review of known results on symplectic fillings and Milnor fibers of quotient surface singularities
Talk 2: 2/15(Thur) Identifying minimal symplectic fillings with Milnor fibers of quotient surface singularities
Talk 3: 2/22(Thur) A Lefschetz fibration viewpoint on minimal
symplectic fillings of quotient surface singularities

Thu Feb 22

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Feb 22

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Feb 21

## PDE Seminar

3:35pm - Vincent Hall 570
Elasticity and curvature: the elastic energy of non-Euclidean thin bodies
Cy Maor, University of Toronto, Canada
##### Abstract:

Non-Euclidean, or incompatible elasticity is an elastic theory for bodies that do not have a reference, stress-free configuration. It applies to many systems, in which the elastic body undergoes inhomogeneous growth (e.g. plants, self-assembled molecules). Mathematically, it is a question of finding the "most isometric" immersion of a Riemannian manifold (M,g) into Euclidean space of the same dimension, by minimizing an appropriate energy functional. Much of the research in non-Euclidean elasticity is concerned with elastic bodies that have one or more slender dimensions (such as leaves), and finding appropriate dimensionally-reduced models for them. In this talk I will give an introduction to non-Euclidean elasticity, and then focus on thin bodies and present some recent results on the relations between their elastic behavior and their curvature.
Based on a joint work with Asaf Shachar.

Wed Feb 21

## Algebraic Geometry

3:35pm - Vincent Hall 301
Algebraic Geometry Seminar

Wed Feb 21

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
The shift functor for FI-modules and its adjoints
Peter Webb, University of Minnesota
##### Abstract:

I will continue with the properties of the adjoint functors of the shift functor following Ramos and Li.

Tue Feb 20

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Feb 20

## Colloquium

2:30pm - Vincent Hall 116
Colloquium

Tue Feb 20

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue Feb 20

## Special Events and Seminars

2:30pm - Ford Hall 130

Tue Feb 20

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Mixed 0-1 linear programs with uncertain objectives: A data-driven approach
Guanglin Xu, University of Minnesota, Twin Cities
##### Abstract:

We study the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent samples can be observed. Using the Wasserstein metric, we construct an ambiguity set centered at the empirical distribution from the observed samples and containing the true distribution with a high statistical guarantee. The problem of interest is to investigate the bound on the expected optimal value over the Wasserstein ambiguity set. Under standard assumptions, we reformulate the problem into a copositive program, which naturally leads to a tractable semidefinite-based approximation. We compare our approach with a moment-based approach from the literature on three applications. Numerical results illustrate the effectiveness of our approach.

Tue Feb 20

## Math Physics Seminar

1:25pm - Vincent Hall 301
The Hyperbolic Restricted 3-Body Problem and Applications to Celestial Mechanics
Harini Chandramouli
##### Abstract:

In this talk we will explore a little history on developments that have been made in the Kepler problem and restricted 3-body problem as we attempt to answer the following question: what would happen if a star passed "close enough" to our solar system to change the orbit of the planets?

Tue Feb 20

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Feb 20

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Feb 20

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Feb 19

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Applied and Computational Math Colloquium

Mon Feb 19

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Forms and Number Theory - Postponed

Speaker
Affiliation:
Abstract:

Mon Feb 19

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Feb 19

## Topology Seminar

2:30pm - Vincent Hall 209
Topology Seminar

Mon Feb 19

## Special Events and Seminars

2:30pm - Vincent Hall 20
Dynamical Systems Seminar - Title: Bifurcations in a Model for Vegetation Patterns
Jasper Weinburd, University of Minnesota
##### Abstract:

We use bifurcation theory to explore a simple model for migrating vegetation bands as observed on gradual slopes of semi-arid grasslands. Our model reproduces this behavior with minimal complexity and mathematically explains the uphill motion. In our analysis we examine the traveling-wave ODE, which turns out to be a tutorial on classic geometric techniques, despite its simplicity. We will focus on the rich bifurcation diagram that results and mention where one could also use methods such as invariant-region phase plane analysis, geometric blow-up, and singular perturbation theory.

Fri Feb 16

## MCFAM Seminar

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

Fri Feb 16

## Special Events and Seminars

3:45pm - Tate Hall 101
Nonoverlapping Domain Decomposition Methods for Saddle Point Problems
Xuemin Tu
##### Abstract:

In this talk, two most popular nonovelapping domain decomposition algorithms will be discussed for solivng a class of saddle point problems arising from mixed finite element or hybridizable discontinuous Galerkin discretizations of partial differential equations. These algorithms reduce the original
saddle point problems to symmetric positive definite problems in a special subspace and therefore the conjugate gradient
methods can be used to accelerate the convergence. The condition numbers for the preconditioned systems are estimated and numerical results are provided to confirm the results.

Fri Feb 16

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Equivariant quantum cohomology of the Grassmannian via rim hooks and puzzles
Kaisa Taipale, University of Minnesota
##### Abstract:

We present a non-recursive, positive combinatorial formulas for expressing the equivariant quantum product in the Schubert basis of the Grassmannian. This extends work of Bertram, Ciocan-Fontanine and Fulton, who provided a way to compute quantum products of Schubert classes of the Grassmannian by applying a combinatorial rimhook rule. Combining our equivariant rule with Knutson and Tao's puzzle rule provides an effective algorithm for computing equivariant quantum Littlewood-Richardson coefficients (polynomials). This rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus.

Fri Feb 16

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Feb 16

## Probability Seminar

2:30pm - Vincent Hall 311
Double Roots of Random Polynomials
Arnab Sen, University of Minnesota
##### Abstract:

We consider random polynomials whose coefficients are independent and uniform on {-1, 1}. We will show that the probability that such a polynomial of degree n has a double root is o(n^{-2}) when n+1 is not divisible by 4 and is of the order n^{-2} otherwise. We will also discuss extensions to random polynomials with more general coefficient distributions and other related open problems.
This is joint work with Ohad Feldheim, Ron Peled and Ofer Zeitouni.

Fri Feb 16

## Analysis and PDE Working Seminar

2:30pm - Vincent Hall 207
Analysis and PDE Working Seminar - Canceled

Fri Feb 16

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Feb 16

## MathCEP Seminar

11:15am - Vincent Hall 113
MathCEP Seminar

Thu Feb 15

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Feb 15

## Colloquium

3:30pm - Vincent Hall 16
WEC Meeting

Thu Feb 15

## Differential Geometry and Symplectic Topology Seminar

1:30pm - Vincent Hall 570
On Symplectic Fillings and Milnor Fibers of Quotient Surface Singularities
Professor Jongil Park, Seoul National University
##### Abstract:

One of active research areas in symplectic 4-manifolds is to cassify symplectic fillings of certain 3-manifolds equipped with a contact structure. Among them, people have long studied symplectic fillings of the link of a quotient surface singularity. Note that the link of a quotient surface singularity carries a canonical contact structure which is also known as the Milnor fillable contact structure. One the other hand, algebraic geometers also have studied Milnor fibers as a general fiber of smoothings for a quotient surface singularity.
In this series of talks, Id like to review basics on symplectic fillings and Milnor fibers of quotient surface singularities. Then I will explain some recent works on symplectic fillings and Milnor fibers of quotient surface singularities. The 1st talk is a review of known results on symplectic fillings and Milnor fibers of quotient surface singularities, and the 2nd talk is about identifying minimal symplectic fillings with Milnor fibers of quotient surface singularities (joint work with Heesang
Park, Dongsoo Shin and Giancarlo Urz´ua). In the 3rd talk, Ill also explain how we interpret minimal symplectic fillings of quotient surface singularities as positive allowable Lefschetz fibrations (joint work with Hakho Choi). A tentative schedule is the following:
Talk 1: 2/8(Thur) A review of known results on symplectic fillings and Milnor fibers of quotient surface singularities
Talk 2: 2/15(Thur) Identifying minimal symplectic fillings with Milnor fibers of quotient surface singularities
Talk 3: 2/22(Thur) A Lefschetz fibration viewpoint on minimal
symplectic fillings of quotient surface singularities

Thu Feb 15

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Feb 15

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Feb 14

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Feb 14

## Algebraic Geometry

3:35pm - Vincent Hall 313
Canonical paths on algebraic varieties
Daniel Litt, Columbia University
##### Abstract:

Given a path-connected topological space X and two points x and y, there is typically no distinguished homotopy classes of paths between x and y. If X is a normal algebraic variety over the complex numbers, however, there is a distinguished linear combination of paths between x and y; there is an analogous statement for a variety over any local field. I'll make this precise and describe many applications to arithmetic and geometry: for example, to explicit descriptions of Galois actions on fundamental groups, and to the study of the geometry of Selmer varieties. Some of the work described is joint with Alexander Betts.

Wed Feb 14

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
More homological properties of FI-modules
Peter Webb, University of Minnesota
##### Abstract:

The #-filtered FI-modules act as a substitute for injective modules in that they are acyclic with respect to certain derived functors. I will discuss the behavior of these FI-modules under some fundamental constructions.

Tue Feb 13

## Colloquium

3:30pm - Vincent Hall 16
Fundamental groups in arithmetic and geometry
Daniel Litt, Columbia University
##### Abstract:

Let X be an algebraic variety -- that is, the solution set to a system of polynomial equations. Then the *fundamental group* of X has several incarnations, reflecting the geometry, topology, and arithmetic of X. This talk will discuss some of these incarnations and the subtle relationships between them, and will describe an ongoing program which aims to apply the study of the fundamental group to classical problems in
algebraic geometry and number theory.

Tue Feb 13

## Colloquium

2:30pm - Vincent Hall 116
Colloquium

Tue Feb 13

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar

Tue Feb 13

## Special Events and Seminars

2:30pm - Ford Hall 130
Undergraduate Mathematics Research Seminar - EMD and Chaos
John Nguyen
##### Abstract:

We explore the effectiveness of a time series algorithm in studying chaotic systems. First we study the effect of forcing on an oceanic model. After the model exhibits chaotic behavior, our focus will shift towards classical chaotic systems and a method of time series signal decomposition tool called the Hilbert-Huang transform. After analyzing decompositions of systems such as the Duffing oscillator and the Lorenz attractor, we end our discussion with an evaluation of the Hilbert-Huang transform.

Tue Feb 13

## Math Physics Seminar

1:25pm - Vincent Hall 301
The n Body Determinant
Peter Olver
##### Abstract:

I will prove two recent conjectures concerning the n body matrix that appears in recent work of Turbiner, Miller, and Escobar--Ruiz on the classical and quantum n body problem. First, whenever the masses are in a nonsingular configuration, meaning that they do not lie on a lower dimensional affine subspace, the n body matrix is positive definite, and hence defines a Riemannian metric on the space coordinatized by the interpoint distances. Secondly, its determinant can be factored into the product of the order n Cayley--Menger determinant and a mass-dependent factor that is of one sign on all nonsingular mass configurations. Characterizing the latter factor and understanding the geometry of the underlying Riemannian space remain open problems.

Tue Feb 13

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Feb 13

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Feb 13

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Feb 12

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Modeling Glioma Growth with fully Anisotropic Diffusion
Thomas Hillen, U Alberta
##### Abstract:

The human brain has a complex geometric structure consisting of white and gray matter, blood vessels, ventricles, skull etc. It forms a highly anisotropic medium. Glioma in the brain are known to invade along white matter tracks and along other brain structures. Using diffusion tensor imaging (DTI) it is now possible to obtain directional information of the brain geometry. In my talk I will show how this DTI information can be used to parametrize a fully anisotropic diffusion equation for glioma spread. We validate the model on clinical data of glioma patients and discuss the future use in treatment design. (joint work with A. Swan, K.J. Painter, C. Surulescu, C. Engwer, M. Knappitsch, A. Murtha).

Mon Feb 12

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Forms and Number Theory

Mon Feb 12

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Feb 12

## Topology Seminar

2:30pm - Vincent Hall 209
Topology Seminar

Fri Feb 09

## MCFAM Seminar

5:30pm - Vincent Hall 16
Optimal Investment to Minimize the Risk of Drawdown
Dongchen Li, University of St. Thomas
##### Abstract:

Drawdown measures an investor's sustained loss from a historic high-water mark (maximum). In fund management industry, drawdown is one of the most frequently quoted indices for downside risks, for instance, in performance measures such as the Calmar ratio and the Ster- ling ratio. Controlling the risk of drawdown is crucial as a significant drawdown or a long period in drawdown (i.e., a long period below historic high-water mark) may trigger large-scale fund redemptions. This presentation focuses on investigating the optimal trading strategies when the objective is to dynamically minimize drawdown-based risk metrics. In particular, probability of drawdown and expected cumulative drawdown are considered. Under the Black-Scholes frame- work, closed-form optimal trading strategies are derived in both cases by utilizing respectively a decomposition technique and Legendre transform on the associated Hamilton-Jacobi-Bellman (HJB) equation. A detailed discussion on the behavior of the optimal trading strategies will be subsequently presented.

Fri Feb 09

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Algebras of quantum monodromy data and decorated character varieties
Leonid Chekhov, Michigan State
##### Abstract:

We discuss the Riemann-Hilbert correspondence for extensions of the de Rham moduli space by allowing connections with higher order poles. We show that geometrically this corresponds to interpreting higher order poles in the connection as boundary components with bordered cusps (vertices of ideal triangles in the Poincaré metric) on the Riemann surface. We thus introduce the notion of decorated character variety. This decorated character variety is the quotient of the space of representations of the fundamental groupid of arcs by a product of unipotent Borel subgroups (one per bordered cusp). We demonstrate that this representation space is endowed with a Poisson structure induced by the Fock-Rosly bracket and show that the quotient by unipotent Borel subgroups giving rise to the decorated character variety is a Poisson reduction. We deal with the Poisson bracket and its quantization simultaneously, thus providing a quantisation of the decorated character variety. In the case of dimension 2, we also endow the representation space with explicit Darboux coordinates. We conclude with a conjecture on the extended Riemann-Hilbert correspondence for higher rank algebras (joint work with M. Mazzocco and V. Rubtsov)

Fri Feb 09

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Feb 09

## Probability Seminar

2:30pm - VinH 311
Probability Seminar

Fri Feb 09

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Fri Feb 09 11:15am - Vincent Hall 113
Video Textbooks In The Active Learning Classroom
Mike Weimerskirch
##### Abstract:

As our computational power increases with each new technological advance, our need for proficiency in higher-order thinking skills grows. That is the thought behind the flipped classroom, which enables instructors to focus on deeper thought processes during class time, while relegating routine tasks to readings, videos and practice that students do outside of the classroom. The standard approach is to record video lectures based on a printed text. A better approach is to begin the instruction with the video as the primary source of imparting information to students. Video offers a greater flexibility in presenting concepts and connecting ideas. The University of Minnesota now uses open source video textbooks to teach its pre-calculus courses in active learning classrooms.

Thu Feb 08

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Feb 08

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Thu Feb 08

## Differential Geometry and Symplectic Topology Seminar

1:30pm - Vincent Hall 570
On Symplectic Fillings and Milnor Fibers of Quotient Surface Singularities
Professor Jongil Park, Seoul National University
##### Abstract:

Abstract
One of active research areas in symplectic 4-manifolds is to cassify symplectic fillings of certain 3-manifolds equipped with a contact structure. Among them, people have long studied symplectic fillings of the link of a quotient surface singularity. Note that the link of a quotient surface singularity carries a canonical contact structure which is also known as the Milnor fillable contact structure. One the other hand, algebraic geometers also have studied Milnor fibers as a general fiber of
smoothings for a quotient surface singularity.
In this series of talks, Id like to review basics on symplectic fillings and Milnor fibers of quotient surface singularities. Then I will explain some recent works on symplectic fillings and Milnor fibers of quotient surface singularities. The 1st talk is a review of known results on symplectic fillings and Milnor fibers of quotient surface singularities, and the 2nd talk is about identifying minimal symplectic fillings with Milnor fibers of quotient surface singularities (joint work with Heesang
Park, Dongsoo Shin and Giancarlo Urz´ua). In the 3rd talk, Ill also explain how we interpret minimal symplectic fillings of quotient surface singularities as positive allowable Lefschetz fibrations (joint work with Hakho Choi). A tentative schedule is the following:
Talk 1: 2/8(Thur) A review of known results on symplectic fillings and Milnor fibers of quotient surface singularities
Talk 2: 2/15(Thur) Identifying minimal symplectic fillings with Milnor fibers of quotient surface singularities
Talk 3: 2/22(Thur) A Lefschetz fibration viewpoint on minimal
symplectic fillings of quotient surface singularities

Thu Feb 08

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Feb 08

## Geometric Analysis Learning Seminar

10:00am - Vincent Hall 570
Geometric Analysis Learning Seminar

Wed Feb 07

## PDE Seminar

3:35pm - Vincent Hall 570
On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds
Alexander Grigor'yan, Bielefeld University, Germany
##### Abstract:

Plan of the talk:
1. Laplace-Beltrami operator and its Green function on a Riemannian manifold.
2. Semi-linear inequality $\Delta u+ F(x) u^\sigma \le 0$.
Pointwise lower bound for positive solutions $u$ via the Green function.
3. Approach to the proof.
4. Existence of positive solutions of $\Delta u+ u^\sigma \le 0$.
Volume test for non-existence. Green function test.
5. Examples of application.
6. Approach to the proof.

Wed Feb 07

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Local cohomology of FI-modules: background
Peter Webb, University of Minnesota
##### Abstract:

I will develop the homological machinery underlying the theory of local cohomology of FI-modules, following work of Ramos, Li-Ramos and Li-Yu.

Tue Feb 06

## Colloquium

2:30pm - Vincent Hall 116
Colloquium

Tue Feb 06

## Colloquium

2:30pm - Vincent Hall 16
Topological Vistas in Neuroscience
Kathryn Hess, École polytechnique fédérale de Lausanne
##### Abstract:

will describe results obtained in collaboration with the Blue Brain Project on the topological analysis of the structure and function of digitally reconstructed microcircuits of neurons in the rat cortex and outline our on-going work on topology and synaptic plasticity. The talk will include an overview of the Blue Brain Project and a brief introduction to the topological tools that we use. If time allows, I will also briefly sketch other collaborations with neuroscientists in which my group is involved.

Tue Feb 06

## Topology Seminar

2:30pm - Vincent Hall 16
Topological vistas in neuroscience (special colloquium)
Kathryn Hess, École polytechnique fédérale de Lausanne
##### Abstract:

I will describe results obtained in collaboration with the Blue Brain Project on the topological analysis of the structure and function of digitally reconstructed microcircuits of neurons in the rat cortex and outline our on-going work on topology and synaptic plasticity. The talk will include an overview of the Blue Brain Project and a brief introduction to the topological tools that we use. If time allows, I will also briefly sketch other collaborations with neuroscientists in which my group is involved.

Tue Feb 06

## Special Events and Seminars

2:30pm - Ford Hall 130

Tue Feb 06

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Bandwidth selection for kernel density estimators of multivariate level sets and highest density regions
Charles Doss, University of Minnesota, Twin Cities
##### Abstract:

We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\RR^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one specifies the probability content of the set rather than specifying the level directly; this complicates the problem. Bandwidth selection for KDEs is well-studied, but the goal of most methods is to minimize a global loss function for the density or its derivatives. The loss we consider here is instead the measure of the symmetric difference of the true set and estimated set. We derive an asymptotic approximation to the corresponding risk. The approximation depends on unknown quantities which can be estimated, and the approximation can then be minimized to yield a choice of bandwidth, which we show in simulations performs well.

Bio:
I am an assistant professor in the School of Statistics of the University of Minnesota. I have worked largely on problems related to nonparametric estimation and inference of density or regression functions. In particular, I have worked on shape-constrained problems, where the function or some transformation of it is concave. Shape constraints serve as natural regularizers and automatically yield many nice properties, and in particular often can lead to estimators that perform automatic tuning parameter selection.

Tue Feb 06

## Math Physics Seminar

1:25pm - Vincent Hall 301
The n Body Determinant
Peter Olver
##### Abstract:

I will prove two recent conjectures concerning the n body matrix that appears in recent work of Turbiner, Miller, and Escobar--Ruiz on the classical and quantum n body problem. First, whenever the masses are in a nonsingular configuration, meaning that they do not lie on a lower dimensional affine subspace, the n body matrix is positive definite, and hence defines a Riemannian metric on the space coordinatized by the interpoint distances. Secondly, its determinant can be factored into the product of the order n Cayley--Menger determinant and a mass-dependent factor that is of one sign on all nonsingular mass configurations. Characterizing the latter factor and understanding the geometry of the underlying Riemannian space remain open problems.

Tue Feb 06

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Feb 06

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Feb 06

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Feb 05

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Modeling and Simulating Nematic Liquid Crystals with Finite Element Methods
Shawn Walker, Louisiana State University
##### Abstract:

This talk begins with an overview of nematic liquid crystals (LCs), including their basic physics, applications, and how they are modeled. We then describe the Ericksen (energy) model of liquid crystals for computing equilibrium configurations (energy minimizers) of liquid crystals with variable degree of orientation. The model consists of a Frank-like energy with an additional
parameter that allows for line defects with finite energy, but leads to a degenerate elliptic equation for the director field. We present a finite element method (FEM) that uses a special discrete form of the energy that does not require regularization of the degenerate part. This allows us to obtain a stable, monotone (gradient flow) scheme for computing minimizers of the energy. Moreover, we are able to show that the discrete energy Gamma-converges to the continuous version, which delivers convergence of the FE scheme. This part of the talk is mainly joint with Ricardo Nochetto and Wujun Zhang.

We then present various numerical simulations and applications of our method, such as simulating LCs in 3-D, modeling collidal inclusions, and including electric effects. We also present a coupled Ericksen/Cahn-Hilliard model to simulate droplets of liquid crystal with (anisotropic) surface tension effects. The phase-field project is joint with Amanda Diegel (post-doc at LSU). I will also discuss another project with summer REU 2017 students (E. Seal and A. Morvant) on coupling the Allen-Cahn equations to the Ericksen model.

Mon Feb 05

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Forms and Number Theory

Mon Feb 05

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Feb 05

## Topology Seminar

2:30pm - Vincent Hall 209
Topology Seminar

Mon Feb 05

## Special Events and Seminars

1:25pm - Vincent Hall 301
Special Combinatorics Seminar

Mon Feb 05

## Combinatorics Seminar

1:25pm - Vincent Hall 301
The Hall Algebra at $t = 1/q$ and Torus Knots
Fri Feb 02

## MCFAM Seminar

5:30pm - Vincent Hall 16
Credit Implied Volatility and Static Arbitrage Free Volatility Surfaces
2018 Modeling Workshop Teams, U of MN MFM 2018 Modeling Workshop
##### Abstract:

Students from two different 2018 modeling teams give a synopsis of their modeling work:

Credit Implied Volatility; Industry Mentor, Dr. Chris Bemis
Students study an intersection of options pricing and fixed income valuation using Merton's structural model approach. They analyze market data in this setting, in particular, CDS spreads. This work leads to viewing complications that arise in several mathematical finance models; viz., non-constant implied volatilities and the poor fit of the log-normal assumption of asset returns. One interesting resolution to these issues may be found in applying recent work by Borland and Bouchaud.
Static Arbitrage Free Volatility Surfaces; Industry Mentor, Roman Borisov
Fitting an equity volatility surface is a fundamental finance problem, and while many techniques exist, they often do not guarantee the absence of static arbitrage. Students learn types of static arbitrage in volatility surfaces and investigate problems involved in creating a model that guarantees no riskless profits. Issues of arbitrage-free interpolation are also explored. As a result students create a functional volatility surface model by using the work of Gatheral and Jacquier. The model belongs to the SVI family and does not admit arbitrage under certain tractable conditions.

Fri Feb 02

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar
Hanbaek Lyu, Ohio State
Fri Feb 02

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Feb 02

## Probability Seminar

2:30pm - VinH 311
Phase transition in the spiked random tensors
Wei-Kuo Chen, UMN
##### Abstract:

The problem of detecting a deformation in a symmetric Gaussian random tensor is concerned about whether there exists a statistical hypothesis test that can reliably distinguish a low-rank random spike from the noise. Recently Lesieur et al. (2017) proved that there exists a critical threshold so that when the signal-to-noise ratio exceeds this critical value, one can distinguish the spiked and unspiked tensors and weakly recover the spike via the minimal mean-square-error method. In this talk, we will show that in the case of the rank-one spike with Rademacher prior, this critical value strictly separates the distinguishability and indistinguishability of the two tensors under the total variation distance. Our approach is based on a subtle analysis of the high temperature behavior of the pure p-spin model, arising initially from the field of spin glasses. In particular, the signal-to-noise criticality is identified as the critical temperature, distinguishing the high and low temperature behavior, of the pure p-spin model.

Fri Feb 02

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Anna Kondic, Merck & Co, Inc.
Fri Feb 02

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Thu Feb 01

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Feb 01

## Colloquium

3:30pm - Vincent Hall 16
A rational blowdown surgery on 4-manifolds
Ordway Visitor - Jongil Park, Seoul National University
##### Abstract:

Since gauge theory was introduced in 1982, people working on 4- manifolds have developed various techniques and surgeries and they have obtained many fruitful and remarkable results on 4-manifolds in last 35 years. Among them, a rational blowdown surgery technique initially introduced by R. Fintushel and R. Stern and later generalized by J. Park turned out to be one of the simple but powerful techniques to construct a new family of 4-manifolds.
In this talk, first Id like to briefly review what we have obtained in 4-manifold topology by using a rational blowdown surgery. And then Ill explain in some details that any minimal symplectic filling of the link of a quotient surface singularity can be obtained by a sequence of rational blowdowns and blowing-ups from the minimal resolution the corresponding quotient surface singularity.

Thu Feb 01

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Feb 01

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Wed Jan 31

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Jan 31

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Homological properties of FI modules - continuation
Peter Webb, University of Minnesota
##### Abstract:

I will continue presenting the recent paper of Liping Li: Two homological proofs of the Noetherianity of FI_G. Last week I reviewed the various functors that appear in the proof of the Noetherian property and this week we will use them.

Tue Jan 30

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Jan 30

## Colloquium

2:30pm - Vincent Hall 116
Colloquium

Tue Jan 30

## Topology Seminar

2:30pm - Vincent Hall 2
Topology Seminar
Weiyan Chen, University of Minnesota, Twin Cities

TBA

Tue Jan 30

## Special Events and Seminars

2:30pm - Ford Hall 130
Constraints on the Oceanic Carbon Sink Using Atmospheric Oxygen Data
Julie Sherman
##### Abstract:

In this study we develop a simple model of the global carbon-oxygen budget in which we incorporate data from the Scripps Carbon Dioxide and Oxygen Programs. Our results are obtained from derivative free optimization techniques, and give minimum sources and sinks necessary to replicate atmospheric observations. We compare our results to large and complex global circulation models.

Tue Jan 30

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Implicit Regularization in Nonconvex Statistical Estimation
Yuxin Chen, Princeton University
##### Abstract:

Recent years have seen a flurry of activity both in theory and practice of nonconvex optimization. Carefully designed nonconvex procedures simultaneously achieve optimal statistical accuracy and computational efficiency for many problems. Due to the highly nonconvex landscape, the state-of-the-art results often require proper regularization procedures (e.g. trimming, projection, or extra penalization) to guarantee fast convergence. For vanilla algorithms, however, the prior theory usually suggests conservative step sizes in order to avoid overshooting.

This talk uncovers a striking phenomenon: even in the absence of explicit regularization, nonconvex gradient descent enforces proper regularization automatically and implicitly under a large family of statistical models. In fact, the vanilla nonconvex procedure follows a trajectory that always falls within a region with nice geometry. This "implicit regularization" feature allows the algorithm to proceed in a far more aggressive fashion without overshooting, which in turn enables faster convergence. We will discuss several concrete fundamental problems including phase retrieval, matrix completion, blind deconvolution, and recovering structured probability matrices, which might shed light on the effectiveness of nonconvex optimization for solving more general structured recovery problems.

This is joint work with Cong Ma, Kaizheng Wang, and Yuejie Chi.

Bio: Yuxin Chen is currently an assistant professor in the Department of Electrical Engineering at Princeton University. Prior to joining Princeton, he was a postdoctoral scholar in the Department of Statistics at Stanford University, and he completed his Ph.D. in Electrical Engineering at Stanford University. His research interests include high-dimensional data analysis, convex and nonconvex optimization, statistical learning, and information theory.

Tue Jan 30

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jan 30

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Jan 30

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Jan 29

## Applied and Computational Math Colloquium

3:35pm - Lind Hall 215
Applied and Computational Math Colloquium

Mon Jan 29

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Meromorphic continuations of solutions of differential equations in automorphic forms
Kim Klinger-Logan, University of Minnesota
Mon Jan 29

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Mon Jan 29

## Topology Seminar

2:30pm - Vincent Hall 209
Topology Seminar

Fri Jan 26

## MCFAM Seminar

5:30pm - Vincent Hall 16
Insurance Regulatory View
John Robinson, Minnesota Department of Commerce
##### Abstract:

The National Association of Insurance Commissioners (NAIC) states the key elements of their mission: Protect the public interest, Promote competitive markets, Facilitate the fair and equitable treatment of insurance consumers, Promote the reliability, solvency and financial solidity of insurance institutions, Support and improve state regulation of insurance.John Robinsons presentation will provide students, faculty and practitioners with information on the following questions:What is regulation?Why is regulation needed?Who are regulators?What does a regulatory Actuary do?How is insurance regulation developed?What is the Valuation Manual?

Fri Jan 26

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar

Fri Jan 26

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Jan 26

## Probability Seminar

2:30pm - VinH 311
Sub-optimality of local algorithms for some problems on sparse random graphs
Mustazee Rahman, MIT
##### Abstract:

Suppose we want to find the largest independent set or maximal cut ina sparse Erdos-Renyi graph, where the average degree is constant. Manyalgorithms proceed by way of local decision rules, for instance, the"nibbling" procedure. I will explain a form of local algorithms that capturesmany of these. Then I will explain how these fail to find optimal independentsets or cuts once the average degree of the graph gets large. There are someconnections to entropy and spin glasses.

Fri Jan 26

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 305
A Tour of Precision Agriculture with Drones, Remote Sensing, and Mathematics
Bryan Poling, Sentek Systems LLC
##### Abstract:

This talk will be a tour of what my company, Sentek Systems LLC, is doing
with drones, remote sensing, and mathematics in the Precision Agriculture
industry. Sentek Systems designs and manufactures multi-spectral cameras
made for use on small unmanned aerial vehicles (drones). We also make
software for image processing and analysis of drone imagery and we con-
duct research in crop management using remote sensing. I will show you
some of the basics of multi-spectral remote sensing and Photogrammetry,
and specifically how it relates to agriculture. I will also take you on a tour
of some of the interesting problems we have come across in our journey.

Fri Jan 26

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Thu Jan 25

## Student Combinatorics Seminar

3:35pm - Vincent Hall 570
Student Combinatorics Seminar
Christine Berkesch Zamaere
Thu Jan 25

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Thu Jan 25

## Differential Geometry and Symplectic Topology Seminar

1:35pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Jan 25

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Wed Jan 24

## PDE Seminar

3:35pm - Vincent Hall 570
Channel of energy inequality and Null concentration of energy for wave maps
Hao Jia, University of Minnesota
##### Abstract:

The channel of energy inequality for linear wave equations was introduced by Duyckaerts-Kenig-Merle to study soliton resolution for the focusing energy critical wave equations. It has been very useful for understanding long time behavior of semilinear wave equations, in the non-perturbative regime. Sometimes, it is the only available tool to understand dispersion of energy in the presence of solitons. Recently we found a new form of this type of inequality for outgoing waves, that turns out to be useful for studying energy critical wave maps, especially in ruling out the so-called `null concentration of energy". In this talk we will give an outline of the inequality, the history of wave maps, explain why the absence of null energy is important, and why channel of energy inequality seems to be uniquely good for ruling out this type of energy concentration. Joint work with Duyckaerts, Kenig and Merle.

Wed Jan 24

## Algebraic Representation Theory Seminar

2:30pm - Vincent Hall 6
Homological properties of FI modules
Peter Webb, University of Minnesota
##### Abstract:

I will introduce recent work of Liping Li that leads to proofs of the Noetherian property of FI-modules and also the local cohomology of FI-modules.

Tue Jan 23

## IMA MCIM Industrial Problems Seminar

4:30pm - Lind 400
Information session for grad students with Cargill and Target
-, -
##### Abstract:

Graduate students are invited to learn about possible careers and internships at Cargill and Target, as well as about the kinds of problems of interest in industrial data science. The event will feature short presentations by members of both companies, a poster session for graduate students, and opportunities for discussion and networking over light refreshments.

Interested participants are asked to RSVP at the Google Form https://goo.gl/x9wztd by Friday, January 19th to allow planning for refreshments and poster set-ups.

Tue Jan 23

## Colloquium

3:30pm - Vincent Hall 116
Colloquium

Tue Jan 23

## Colloquium

2:30pm - Vincent Hall 116
Colloquium

Tue Jan 23

## Topology Seminar

2:30pm - Vincent Hall 2
Quantum Deformation Theory
Sasha Voronov, University of Minnesota, Twin Cities
##### Abstract:

Classical deformation theory is based on the Classical Master Equation (CME), a.k.a. the Maurer-Cartan Equation: dS + 1/2 [S,S] = 0. Physicists have been using a quantized CME, called the Quantum Master Equation (QME), a.k.a. the Batalin-Vilkovisky (BV) Master Equation: dS + h \Delta S + 1/2 {S,S} = 0. The CME is defined in a differential graded (dg) Lie algebra, whereas the QME is defined in a space V[[h]] of formal power series or V((h)) of formal Laurent series with values in a dg BV algebra V. One can anticipate a generalization of classical deformation theory arising from the QME, quantum deformation theory. Quantum deformation functor and its representability will be discussed in the talk.

Tue Jan 23

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Tue Jan 23

## Student Number Theory Seminar

11:15am - Vincent Hall 313
Student Number Theory Seminar

Tue Jan 23

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 364

Mon Jan 22

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 364
Automorphic Form and Number Theory

Mon Jan 22

## Math Biology Seminar

3:35pm - Vincent Hall 213
The Lubricated Immersed Boundary Method
Thomas Fai
##### Abstract:

Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.

Mon Jan 22

## Cockburn's Seminar

3:30pm - Ford Hall B10
Cockburn's Seminar

Fri Jan 19

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar - Canceled

Fri Jan 19

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Affine Growth Diagrams
Tair Akhmejanov, Cornell
##### Abstract:

We introduce a new type of growth diagram, arising from the geometry of the affine Grassmannian for $GL_m$. These affine growth diagrams are in bijection with the $c_{\vec\lambda}$ many components of the polygon space Poly($\vec\lambda$) for $\vec\lambda$ a sequence of minuscule weights and $c_{\vec\lambda}$ the Littlewood--Richardson coefficient. Unlike Fomin growth diagrams, they are infinite periodic on a staircase shape, and each vertex is labeled by a dominant weight of $GL_m$. Letting $m$ go to infinity, a dominant weight can be viewed as a pair of partitions, and we recover the RSK correspondence and Fomin growth diagrams within affine growth diagrams. The main combinatorial tool used in the proofs is the $n$-hive of Knutson--Tao--Woodward. The local growth rule satisfied by the diagrams previously appeared in van Leeuwen's work on Littelmann paths, so our results can be viewed as a geometric interpretation of this combinatorial rule.

Fri Jan 19

## Lie Theory Seminar

3:30pm - Vincent 364
Lie Theory Seminar

Fri Jan 19

## Probability Seminar

2:30pm - Vincent 311
Random walks on ultra-metric spaces
Alexander Grigor'yan, Universität Bielefeld
##### Abstract:

Plan of the talk:1. Jump processes and jump kernels. Heat kernel (=transition density) of jump processes. Examples.2. Ultra-metric spaces. Properties of balls in ultra-metric spaces.3. Isotropic jump kernels and the corresponding heat kernels.4. Heat kernel bounds on regular ultra-metric spaces.5. Tail condition and Poincare inequality for jump process. Heat kernel bounds under these condition.6. Some examples.7. Semi-bounded jump kernels.

Fri Jan 19

## IMA MCIM Industrial Problems Seminar

1:25pm - Lind 409
Why Data Science Fails
Scott Ernst, When I Work
##### Abstract:

We hear stories of data science successes all the time, but stories of data science failures are becoming more common as well. As hype gives way to reality, businesses are increasingly scrutinizing their data science investments. But why do some teams succeed while others fail? Well dive into the key attributes that set success apart from failure using a framework that originated in the aftermath of the dot-com crash and helped guide companies like Facebook, LinkedIn, YouTube, Reddit, Zillow and Twitter.

Scott is currently the Director of Data Science & Data Engineering at When I Work, a Minneapolis-based startup. He has a PhD in computational physics that focused on large-scale astrophysical and magnetohydrodynamic plasma simulations. Over the last decade Scott has worked in various data science and engineering roles, which included leading the data science team for an international research project modeling dinosaur behavior on the worlds largest dinosaur track-site. He has also worked as a data visualization artist, creating 3D digital visualizations for clients all over the world including National Geographic, National Public Radio (NPR), Carnegie Natural History Museum, Los Angeles Natural History Museum, Asahi Shimbun (????), Tokyo Natural History Museum and Jurassica in Switzerland.

Fri Jan 19

## Commutative Algebra Seminar

12:20pm - Vincent Hall 209
Commutative Algebra

Thu Jan 18

## Student Combinatorics Seminar

4:30pm - Vincent Hall 301
Student Combinatorics Seminar

Thu Jan 18

## Colloquium

3:30pm - Vincent Hall 16
Heat kernels on Riemannian manifolds
Alexander Grigor'yan, Universität Bielefeld
##### Abstract:

Plan of the talk:1. Heat kernels for elliptic operators in $R^n$.2. Laplace-Beltrami operator and its heat kernel.3. Gaussian estimate of the heat kernel in integrated form (Davies-Gaffney).4. Li-Yau estimate of the heat kernel. Necessary and sufficient condition in terms of volume doubling and Poincare inequality.5. Examples of manifolds satisfying Li-Yau estimate.6. Manifolds with ends.7. Parabolic and non-parabolic manifolds.8. Heat kernels on manifolds with ends.

Thu Jan 18

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Jan 18

## Applied and Computational Math Colloquium

11:15am - Tate Hall B20
Structure preserving numerical methods for nonlinear partial differential equations modeling complex fluids
Franziska Weber, U Maryland
##### Abstract:

Nonlinear partial differential equations (PDEs) emerge as mathematical descriptions of many phenomena in physics, biology, engineering, and other fields. Despite lots of research efforts, there are still many open questions in the understanding of nonlinear PDEs. This can be attributed to the complex behavior that solutions of nonlinear PDEs exhibit: They develop singularities of various type, such as shock waves, blow-ups and rapid oscillations.This also poses a challenge for the design of efficient numerical methods for nonlinear PDEs: Good numerical methods should be stable and efficient but at the same time capture the true physical behavior and singularities that the solution may display. To achieve this, it is crucial to mimic properties that the continuous solution of the PDE has  for example, physical constraints or energy balances  a