### Colloquium

Louis H Kauffman, University of Illinois Chicago

Friday, March 22, at 4:10pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**Introduction to Virtual Knot Theory**

Abstract: Virtual knot theory studies the knot theory of embeddings of circles in thickened surfaces. By taking projections of the knot diagrams in surfaces to the plane one obtains a theory of diagrams that contain classical knot crossings and virtual crossings that are neither over nor under. The virtual crossings are an artifact of the projection of the knot to the plane but are very useful for the combinatorial topology. Virtual crossings also occur in planar projections of non-planar graphs, and there are many analogies between graph theory and knot theory in this domain. The talk will discuss invariants of virtual knots such as the Jones polynomial in Kauffman bracket form, the odd writhe, the Manturov Parity Bracket, the Arrow polynomial and the Affine Index Polynomial. This theory has many interesting examples and many relations with classical knot theory

and with combinatorics and graph theory. The talk will be self-contained.

### Statistics Seminar

Timothy Keller, SLU

Tuesday, February 26 at 2:30pm in Ritter 106.

**Sampling, Elephants, Agricultural Estimates, and Survey Non-Response**

A brief discussion of the Horvitz-Thompson Theorem and its relation to survey sampling theory in practice is presented, followed by an application that illustrates the issues of making estimates when one doesn't have the sort of data one would like to have.

The talk should be accessible at the level of an undergraduate who has completed a calculus based introductory statistics course, but will also introduce an applied research topic.

### Colloquium

Tyler Bongers, Washington University in Saint Louis

Friday, March 1 at 4:10pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**Stretching and rotation properties of quasiconformal maps**

Abstract: Quasiconformal maps in the plane are homeomorphisms that satisfy useful distortion inequalities: they map infinitesimal circles to ellipses. These maps arise naturally in complex dynamics and geometric function theory, as well as the study of elasticity and elliptic PDEs. In this talk, we will consider the local geometric properties of these maps and discuss the construction of extremizers for certain geometric regularity conditions related to stretching and rotation. This work will improve upon recent results of Astala-Iwaniec-Prause-Saksman and Hitruhin.

### Colloquium

Liberty Vittert, Washington University in Saint Louis

Friday, February 15 at 4:10pm in Ritter 202 with refreshments beforehand in the Ritter Hall Lobby.

**How to Empower the Public to Understand Numbers**

Abstract: Trying to explain your work to the general public can vary between glazed eyes and genuine fear of the subject. What the public doesn’t understand is that they themselves use statistics and probability every single day- from deciding whether to take an umbrella or which route to drive to work- every person performs some kind of statistical or risk analysis on any given day.

This is a subconscious computation, but with the amount of information currently being measured, ‘fake news’ being reported, and a general miscommunication (if not deliberate mislead) of the facts, how do we help the public understand the power of statistics?

We simplify the numbers enough to empower individuals to feel that they themselves know what questions they should be asking of the data. Sometimes we have to walk a thin line between being “correct” and understandable. How do we do that?

### Colloquium

Xiang Tang, Washington University in Saint Louis

*Note different day of week!* Tuesday, January 29 at 4:10pm in Ritter 202 with refreshments beforehand in the Ritter Hall Lobby.

**An Analytic Grothendieck Riemann Roch Theorem**

Abstract: In this talk, we will introduce an interesting index problem naturally associated to the Arveson-Douglas conjecture in functional analysis. This index problem is a generalization of the classical Toeplitz index theorem, and connects to many different branches of Mathematics. In particular, it can be viewed as an analytic version of the Grothendieck Riemann Roch theorem. This is joint work with R. Douglas，M. Jabbari, and G. Yu.

### Colloquium

Daniel Spector, National Chiao Tung University in Hsinchu, Taiwan

Friday, January 18 at 4:00pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**New Directions for Harmonic Analysis on L ^{1}**

Abstract: Classical work in harmonic analysis has led us to a thorough understanding of the right spaces from the standpoint of singular integral operators, in the most basic setting, L^{p} spaces and the Hardy space H^{1}. These spaces, in turn, can be used for estimates of integral operators such as the Newtonian and Riesz potentials. Interestingly, in the endpoint p=1 the Hardy space is not necessary to obtain such an estimate, as one can make a weaker assumption and obtain the same strength of conclusion. In this talk we discuss this phenomena, past and present, and give an idea of what might be in its future.

### Geometry-Topology Seminar

TIME+DATE : 4:10pm--5:00pm Tue 27 Nov 2018

ROOM : 216 Ritter Hall

TITLE: Lie Representation Theory, Frames, and Wavelets, I: Introduction

SPEAKER: Brent Wessel, SLU

ABSTRACT: An important topic when studying Lie groups is the representation theory behind it and how we can relate representations to orbits of certain actions. I will give an overview of the construction and decomposition of wavelet representations of a certain class of nilpotent groups. These will then be used to develop a Calderon condition for the existence of admissible vectors for these groups. The first talk will be focused on some of the background in Lie and representation theory while the second talk will zoom in on a particular class of examples. Graduate students with first-year analysis, topology, and algebra are encouraged to attend, especially the first talk on the background information.

### Math-CS club

TIME+DATE: 4:10-5:00pm Wed 11/28

ROOM : Ritter TBD

Title: Info session on REU in computational arithmetic dynamics

Speaker: Benjamin Hutz, SLU

### Geometry-Topology Seminar

TIME+DATE : 4:10pm--5:00pm Tue 04 Dec 2018

ROOM : 216 Ritter Hall

TITLE: Lie Representation Theory, Frames, and Wavelets, II: Oscillator Groups

SPEAKER: Brent Wessel, SLU

ABSTRACT: An important topic when studying Lie groups is the representation theory behind it and how we can relate representations to orbits of certain actions. I will give an overview of the construction and decomposition of wavelet representations of a certain class of nilpotent groups. These will then be used to develop a Calderon condition for the existence of admissible vectors for these groups. The first talk will be focused on some of the background in Lie and representation theory while the second talk will zoom in on a particular class of examples. Graduate students with first-year analysis, topology, and algebra are encouraged to attend, especially the first talk on the background information.

### Math/CS Club

Integration Bee

Wednesday, November 14 at 4:00pm in the Ritter Hall Lobby.

All undergraduates are invited to compete in the annual Integration Bee. Solve integrals for fabulous prizes!

### Colloquium

Shmuel Weinberger, University of Chicago

Wednesday, November 14 at 3:30pm in Ritter 202 with refreshments beforehand in the Ritter Hall Lobby.*NOTE DIFFERENT TIME AND DAY.*

**Quantitative Topology?**

Abstract: Topology is ordinarily thought of as a qualitative subject - can one map be deformed into another? Are these two spaces homomorphic? However, Rutherford said, "Qualitative is nothing but poor quantitative." I would like to discuss some issues that arise when trying to make topology quantitative.

### SLAMS Inaugural Meeting

Wednesday, November 14 at 6pm. Pere Marquette Gallery, DuBourg Hall, 221 N Grand Blvd on the campus of Saint Louis University.

The Saint Louis Academy of Mathematical Sciences is a gathering of researchers in all areas of the mathematical sciences in the Saint Louis region.

Talk at 6 pm: Efim Zelmanov, UCSD

**Infinite dimensional algebras and superalgebras**

Abstract: We will discuss examples, classification and representations of some infinite dimensional superalgebras that arise in Physics.

7:30 pm dinner, jointly hosted by WUSTL and SLU

Talk open to the public. RSVP required for dinner.

### Geometry-Topology Seminar

TIME+DATE : 4:10pm--5:00pm Tue 06 Nov 2018

ROOM : 216 Ritter Hall

TITLE: Fibrations with Aspherical Fiber, II: Invariants

SPEAKER: Seth Arnold, SLU

ABSTRACT: Given an aspherical CW complex *A*, we determine the homotopy groups of the space of self-homotopy equivalences of *A* using elementary obstruction theory arguments. In order to use obstruction theory, tools are developed to deal with the topologies of function spaces. Using a result of J.P. May that classifies *A*-fibrations up to fiber homotopy equivalence over a connected CW complex, we develop two complete cohomological invariants to distinguish such fibrations.

Graduate students who have taken or plan to take General Topology II (fundamental group and covering spaces) are encouraged to attend. Graduate students are also encouraged to give a later talk about their research or about an interesting fact in geometry or topology.

### Geometry-Topology Seminar

TIME+DATE : 4:10pm--5:00pm Tue 30 Oct 2018

ROOM : 216 Ritter Hall

TITLE: Fibrations with Aspherical Fiber, I: Automorphisms

SPEAKER: Seth Arnold, SLU

ABSTRACT: Given an aspherical CW complex *A*, we determine the homotopy groups of the space of self-homotopy equivalences of *A* using elementary obstruction theory arguments. In order to use obstruction theory, tools are developed to deal with the topologies of function spaces. Using a result of J.P. May that classifies *A*-fibrations up to fiber homotopy equivalence over a connected CW complex, we develop two complete cohomological invariants to distinguish such fibrations.

Graduate students who have taken or plan to take General Topology II (fundamental group and covering spaces) are encouraged to attend. Graduate students are also encouraged to give a later talk about their research or about an interesting fact in geometry or topology.

### Colloquium

Christopher Connell, Indiana University

Friday, November 2 at 4:00pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**Homological Norms on Nonpositively Curved Manifolds**

Abstract: The Gromov-Thurston norm on the singular homology of a closed manifold provides a topological notion of “volume” for a homology class. On the other hand, every such homology class has a dual cohomology class that can be represented by a unique harmonic differential form (with respect to a Riemannian metric) representing that class via the de Rham isomorphism. Forms come equipped with a natural L^{2} norm, and the harmonic norm is the L^{2} norm of this harmonic form. In joint work with Shi Wang, we relate the Gromov-Thurston norm on homology to the harmonic norm on cohomology with upper and lower bounds that depend (necessarily) on the volume and injectivity radius for nonpositively curved manifolds. This extends work of Brock and Dunfield as well as work of Bergeron, Sengun and Venkatesh. We also will discuss some consequences of this relationship between the norms.

### Geometry-Topology Seminar

TIME+DATE : 4:10pm--5:00pm Tue 16 Oct 2018

ROOM : 216 Ritter Hall

TITLE: **A Proof of Gilman's Conjecture**

SPEAKER: Andrew Eisenberg, SLU

ABSTRACT: This talk will cover new research but should still be accessible to graduate students. I will discuss joint work with Adam Piggott proving Gilman's conjecture: any group presented by a finite, monadic, confluent rewriting system must be a free product of finite groups and free groups.

### Colloquium

Kenneth Jacobs, Northwestern

Friday, October 19 at 4:00pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**Reduction Modulo Infinity**

Abstract: Reduction modulo a prime number p is a very useful tool in arithmetic geometry, and recently it has been applied to study the dynamics of rational maps with algebraic coefficients. Several authors have presented methods for determining when a given rational map has potential good reduction and / or semistable reduction, both of which describe degeneracy that arises when reducing modulo p. By adapting the method of R. Rumely (UGA), we are able to give new, parallel notions of good reduction / semi-stable reduction for rational maps having arbitrary complex coefficients.

### Geometry-Topology Seminar

TIME+DATE : 4:10pm--5:00pm Tue 09 Oct 2018

ROOM : 216 Ritter Hall

TITLE: **Rewriting Systems and Gilman's Conjecture**

SPEAKER: Andrew Eisenberg, SLU

ABSTRACT: This will be a background talk, introducing basic definitions and properties of rewriting systems. Rewriting systems are a way of presenting groups with an eye towards answering algebraic and geometric questions algorithmically. A fundamental goal is to understand how features of groups are encoded by different types of rewriting systems. I'll discuss a collection of related results over the past 40 years and introduce Gilman's conjecture on finite, monadic, confluent rewriting systems.

### Colloquium

Elodie Pozzi, Saint Louis U.

Friday, October 5 at 4:00pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**A 2D inverse problem in magnetism**

Abstract: Inverse problems have known a recent development in many fields like signal processing, medical imaging and more recently paleomagnetism. Broadly speaking, an inverse problem consists in reconstructing from a set of measurements the original source. We consider a 2D inverse problem in magnetism to estimate the net moment represented by the mean value of a function supported on an interval K of the real line from the partial knowledge of the magnetism on an another interval S located on the parallel line to K at height h>0. We will see how this question can be rephrased using complex analysis, harmonic analysis and operator theory. To estimate the mean value, we will construct and solve a constrained approximation problem. This talk is based on a joint work with Juliette Leblond, INRIA, France.

### Geometry-Topology Seminar

TIME+DATE : 4:10pm--5:00pm Tue 02 Oct 2018

ROOM : 216 Ritter Hall

TITLE: **Compact Hausdorff groups are pro-Lie, II: the proof**

SPEAKER: Qayum Khan, SLU

ABSTRACT: This is a learning talk, continuing the definitions / statements / discussions of Tue 25 Sep 2018. We go through the Pontrjagin--Weil proof of von Neumann's 1933 theorem, that any compact Hausdorff group is the projective limit of Lie groups, using the Peter--Weyl theorem from classical harmonic analysis.

Graduate students who have taken or are taking General Topology I (point-set topology) are encouraged to attend. Graduate students are also encouraged to give a later talk about their research or about an interesting fact in geometry or topology.

### Algebra Seminar

Katie Radler, SLU graduate student

Thursday, September 27 from 10:00am-11:00am in Ritter 106

**On Prufer-like Properties of Leavitt Path Algebras**

Abstract: In this talk we show two characterizing properties of a Prufer domain that hold in a Leavitt path algebra and we show that the cancellation property does not hold in general with a counterexample. We end with necessary and sufficient conditions on a graph so that the Leavitt path algebra of the graph satisfies the cancellation property.

### Statistics Seminar

Tim Keller, Saint Louis U.

Thursday, September 27 from 3:00-4:00pm in Ritter 204

**Stratified Simple Random Sampling with Multiple Estimation Objectives**

Abstract: Non-response is the greatest challenge facing establishment surveys. A major contributing factor for survey non-response is respondent burden. To meet this challenge survey establishments must therefore strive to meet estimation goals with the smallest possible sample size.

A common and basic survey design is the stratified simple random sample, and a common estimate of interest is the population total for a survey item. For this special case, the problem of meeting multiple estimation objectives is formulated as a convex optimization problem, and a numerical method for determining the optimal allocation of a fixed overall sample size is presented.

### Colloquium

Keri Kornelson, Oklahoma.

Friday, September 21 at 4:00pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**Norm retrieval via spatiotemporal samples**

Abstract: There is a relaxation of the problem of phase retrieval in which the magnitude of a signal is computed from phaseless measurements. We require less information, so can be possible with fewer measurements than phase retrieval. As a ready example, an orthonormal basis yields norm retrieval measurements. In this talk, we introduce the concepts and earlier results about performing phase and norm retrieval in real, finite-dimensional space. We then present recent work with Fatma Bozkurt in which we do norm retrieval with dynamical samples, i.e. samples obtained at selected measurement points but repeated over time.

### Geometry-Topology Seminar

Qayum Khan, Saint Louis U.

Tuesday, September 25, 4:10pm-5:00pm in Ritter Hall 216

**Compact Hausdorff groups are pro–Lie**

Abstract: This is a learning talk. We go through the Pontrjagin–Weil proof of von Neumann's 1933 theorem, that any compact Hausdorff group is the projective limit of Lie groups, using the Peter–Weyl theorem from classical harmonic analysis. Graduate students who have taken or are taking General Topology I (point-set topology) are encouraged to attend. Graduate students are also encouraged to give a later talk about their research or about an interesting fact in geometry or topology.

### Colloquium

- Friday, September 7 at 4:00pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.
- Haiyan Cai, UMSL.
- Classification and Hypothesis Testing
- Abstract: Robust classification algorithms (random forests, support vector machines, deep neural networks, for example) have been developed in recent years with great success. To take advantage of this development , we recast the classical two-sample test problem in the framework of a classification problem. Based on the estimates of class probabilities from a classifier trained from the samples, we propose a new method for the two-sample test. We explain why such a test can be a powerful test and compare its performance in terms of power and efficiency with those of some other recently proposed tests with some simulation and real-life data. Our method is nonparametric and can be applied to complex and high dimensional data whenever there is a good classifier that provides uniformly consistent estimate of class probabilities for such data. The talk will start with a general introduction of the classification problem in machine learning and the basic concepts in hypothesis testing in statistics.

### Geometry-Topology Seminar

- TIME+DATE : 4:10pm--5:00pm Tue 04 Sep 2018
- ROOM : 216 Ritter Hall
- TITLE: Metric spaces are paracompact
- SPEAKER: Qayum Khan, SLU
- ABSTRACT: This is a learning talk. We go through Mary Ellen Rudin's clever one-page proof of Stone's theorem, which states that all metric spaces are paracompact. We will review all necessary definitions. Graduate students who have taken or are taking General Topology I (point-set topology) are encouraged to attend.