### 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.