**Association for Women in Math Student Chapter**

Monday, November 13, 4:10-5:10 in Ritter 323. Refreshments will be served.

Description: In the Sepeaker Series, AWM student chapter is inviting women mathematicians to talk about theri research and to share the challenges they faced as a minority in academia.

Speaker: **Özlem Ugurlu, SLU**

Title: An Introduction to Ehrhart Theory

Given an integer polytope, one can be interested in enumerating the number of integer lattice points contained in the polytope. Further, given any nonnegative integer, one can wish to enumerate the number of integer lattice points contained in the dilated version of the polytope. In the 1960s, Ehrhart put light on these and proved that this counting function is given as a polynomial in the dilation factor of the polytope, the so-called Ehrhart polynomial. In this talk, I will give a brief introduction to the Ehrhart theory. I will go through some of the most important results, including the meaning of specific coefficients, in particular the relation to the arbitrary volume of the polytope, and a nice interpretation of evaluations of the Ehrhart polynomial at negative integers.

**Colloquium**

Friday, November 10, 4:00-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Speaker: **Mee Seong Im, US Naval Academy**

Title: Correspondence Between Automata and One-dimensional Boolean Topological Theories and TQFTs**Abstract: ** Automata are important objects in theoretical computer science. I will describe how automata emerge from topological theories and TQFTs in dimension one and carrying defects. Conversely, given an automaton, there is a canonical Boolean TQFT associated with it. In those topological theories, one encounters pairs of a regular language and a circular regular language that describe the theory.

**Math Club**

Wednesday, November 8, 4:00-5:00 in Ritter Lobby. Pizza and drinks will be available in the Ritter Lobby starting at 3:30. Everyone is welcome!

Speaker: **Nikki Freeman, UNC Chapel Hill**

Title: A friendly introduction to Precision Medicine

Description: Nikki Freeman is a bio-statistician at UNC Chapel Hill, and she will introduce us to what is precision medicine and present on one of her recent projects.

Everyone is welcome!

**Colloquium**

Friday, November 03, 4:00-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Speaker: **Ander Beristain, SLU**

Title: The application of integral calculus, nonlinear regression, and Bayesian inference in understudied speech communities and phenomena

In this talk, I will provide evidence for the application of mathematical and statistical concepts in speech variables that concern understudied communities and phenomena in the world. The three areas in utilization are (i) integral calculus, (ii) nonlinear regression, and (iii) Bayesian inference. Integral calculus will be employed to observe speech aerodynamics and airflow production in Spanish-English bilingual speakers in the US (Beristain, 2023); a nonlinear regression analysis will be presented to study fundamental frequencies (f0) and pitch contours in three rural Basque varieties in the Basque Country, Spain (Hualde, Beristain, & Icardo Isasa, in press); and Bayesian inference will serve to provide a probabilistic estimate regarding ongoing sound merger processes in two rural Basque varieties by analyzing the first spectral moment, i.e., the center of gravity (Beristain, 2022). Attendees will leave the session with a clearer perspective on how to apply mathematical and statistical components in speech sciences.

**Association for Women in Math Student Chapter**

Monday, October 30, 4:30-5:30 in Ritter 323. Refreshments will be served.

We are thrilled to invite you to an exciting and creative event: Pumpkin Painting! As autumn's vibrant colors surround us, what better way to celebrate the season than by getting together to unleash our artistic talents on some pumpkins.

**Association for Women in Math Student Chapter**

Monday, October 23, 4:30-5:30 in Ritter 323. Refreshments will be served.

Speaker: **Lauren Miller, SLU**

Zines∩ math:

Dr. Lauren miller had been using zines in her classroom for over 3 years. They are also a major part of her ignite seminar mathematics through literature. Dr. Miller will be talking with us about zines: what they are, their history, and how they can be used as a learning tool. Together we will design and create individual math zines. As a group we will create a zine about the awm, for recruitment and educational purposes! This zine will be shared with slu’s math magazine, for all.

**Frame Theory Day Conference **

Saturday, October 21th, 9:00 am -5:00 pm in Ritter 323.

A Frame Theory Day Conference will be hosted at SLU. Dorsa Ghoreishi, Daniel Freeman and Brody Johnson are part of the organizing team. The idea of this conference is to get together the researchers in this field from the nearby schools. For more information, contact the organizers.

For more information, check out the conference website.

**Colloquium**

Friday, October 20th, 4:00-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Speaker: **Rocío Díaz Martín, Vanderbilt University**

Title: Bridges between Dynamical Sampling and Control Theory

We will introduce the Dynamical Sampling Problem and explore its connections with the Observability Problem in Control Theory. We will see that in both cases the task is essentially that of recovering the initial state of a dynamical system. To establish a "dictionary" between these two areas, we will review key concepts such as exact and approximate controllability, Gramian matrices, Bessel sequences in Hilbert spaces, and frames. By analyzing the interplay between these two viewpoints of the same problem, we will uncover relations between discrete-time and continuous-time dynamical systems, utilizing insights from both fields and our established dictionary. Additionally, time permitting, we will present a simple method, based on Kalman filter techniques, for estimating the initial state of a linear dynamical system using noisy observations. We will be covering aspects of joint work with Akram Aldroubi (Vanderbilt University, Nashville, TN, USA), Ivan Medri (TSU, Nashville, TN USA), Ursula Molter (UBA, Buenos Aires, Argentina), and Juliana Osorio (UBA, Buenos Aires, Argentina).

**Association for Women in Math Student Chapter**

Monday, October 16, 4:30-5:30 in Ritter 323. Refreshments will be served.

Graduate Student Speakers: **Alina Abdurakhimova, Sydney Bement, and Olivia Frank**

Predciting taylor swift songs using markov chains this paper presents an approach to the analysis of taylor swift's discography by employing markov chains. Taylor swift, one of the most prolific and influential artists of our time, has a diverse and evolving musical career spanning multiple genres. Markov chains, a mathematical model used in various fields, including music, can be applied to study the evolution of her themes and musical styles throughout her career.

**Colloquium**

Friday, October 13th, 4:00-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Speaker: **Sam Walsh, University of Missouri-Columbia**

Title: Traveling water waves

In this talk, we will give a very broad introduction to the mathematical theory of steady water waves with a particular focus on progress made in the past few decades and major open problems. While water waves are described by nonlinear PDEs, their study draws on ideas from many areas. Indeed, they served as a major motivation for Cauchy's work in complex analysis. Modern investigations rely on tools from dynamical systems such as bifurcation theory and invariant manifolds. We will also discuss applications of global bifurcation theory based on topological degree theory or the structural properties of analytic varieties.

**Association for Women in Math Student Chapter**

Monday, October 9, 4:30-5:30 in Ritter 323. Refreshments will be served.

Description: In the Sepeaker Series, AWM student chapter is inviting women mathematicians to talk about theri research and to share the challenges they faced as a minority in academia.

Speaker: **Elodie Pozzi, SLU**

Title: The Composition Operator

Any calculus student has already studied the composition of two functions f o g(x)=f(g(x)) for example, when differentiating the resulting function, or by making a substitution in an integral. If the inner function g is fixed, what can be said about the action of composing any function by g? To answer this question, one can study the mechanism of composition by a fixed function by considering the linear map f---> fog called the composition operator. In this talk, we will give several properties of this map with some applications and the role of the composition operator in the theory of linear maps.

**Education Colloquium**

Friday, October 6th, 4:00-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Speaker: **Mary Silverglate, Lindenwood University**

Title: Why Johnny Still Can’t Add: How America’s K-12 Math Curriculum Effects Student Readiness in the College Math Classroom.

**Association for Women in Math Student Chapter**

Monday, October 2nd, 4:00-5:00 in Ritter 323. Refreshments will be served.

Description: In the Sepeaker Series, AWM student chapter is inviting women mathematicians to talk about theri research and to share the challenges they faced as a minority in academia.

Speaker: **Stacey Harris, SLU**

Title: Spacetimes, Boundaries, and Generalizations

A spacetime represents the persistence of objects through time: each point of spacetime is an event, and an object is a curve of such events; but there is added structure that encodes the physical observation that nothing travels faster than photons (particle of light). We'll look at some simple examples, including both "static" spacetimes physics unchanging in time) and the interior of the

simplest black hole, including the singularity (a boundary on the spacetime, not part of the spacetime proper, as a spacetime is a manifold). We'll then consider a couple approaches to generalizations of spacetime. One approach looks at the question of continuous (but not differentiable) extension beyond a putative singularity. The other looks at consideration of a generalization beyond manifolds, a "Lorentzian Length Space"; this allows one to model the physics of singular boundary points (such as cone singularities).

**Education Colloquium**

Friday, September 22th, 4:00-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Description: In this education colloquium, two of our faculty members will share their experience with running Ignite Seminars at SLU.

Speaker: **Benjamin Hutz & Lauren Miller, SLU**

Title: On Ignite Seminars

**Math Club**

Wednesday, September 20th, 4:00-5:00 in Ritter Lobby. Pizza and drinks will be available in the Ritter Lobby starting at 3:30.

Description: We will be playing Math Balderdash this week.

People will break up into teams and try to answer fun questions. Most likely you will not know the solutions and will have to guess. Each team will submit an answer on a piece of paper and I will also write down the correct answer on a piece of paper. The pieces of paper will be mixed up and then read out loud and you will have to vote on what answer you think is the correct one. You will get points for guessing correctly and points for tricking other people to vote for your answer!

**Colloquium**

Friday, September 15th, 4:00-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Description: In this colloquium, each of our two faculty members will give a 15-minute talk about their research areas.

Speaker: **Michael Landry, SLU**

Title: Flows and foliations in 3-manifolds

With the resolution of several important conjectures in 3-dimensional topology, interest has swelled in the types of geometric and dynamical objects that live in 3-manifolds and their interrelations. I will discuss some of the objects that arise naturally when a 3-manifold fibers over the circle, and explain how this picture motivates several areas of active research.

Speaker: **Dorsa Ghoreishi, SLU**

Title: Frame Theory and Phase Retrieval

Frames, like orthonormal bases, give a continuous, linear, and stable reconstruction formula for vectors in a Hilbert space. However, frames allow for redundancy, and this makes frames much more adaptable for theory and applications. Phase retrieval is an application of frame theory which is prominently used in X-ray crystallography and coherent diffraction imaging where only the intensity of each linear measurement of a signal is available and the phase information is lost. The goal of phase retrieval is to recover these lost phases up to some universal global factor. In this talk, I will be introducing this area of reseach and will present some of the research topics that are suitable for undergraduate and graduate student researchers.

**Colloquium**

Friday, September 8th, 4:00-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Description: In this colloquium, each of our three faculty members will give a 15-minute talk about their research areas.

Speaker: **Darrin Speegle, SLU**

Title: Meyer-type wavelets for integer dilations

Given a matrix A, an A wavelet is a function f from R^n to R such that if you dilate the function by powers of A and translate by integers, then you obtain an orthonormal basis for L^2(R^n). In my research, I have been interested in questions about wavelets that involve the geometric relationship between the actions of two groups on R^n; namely, the groups A^j acting multiplicativel

Speaker: **Hugo Panzo, SLU**

Title: Geometric functionals of the planar Brownian convex hull and related inverse processes

Study of the convex hull of planar Brownian motion was initiated by Lévy in the 1940's, and since then, several striking results have been proved such as exact formulas for its average perimeter and area. Conversely, the inverse processes of perimeter, area, and other geometric functionals have been investigated only recently and not much is known besides some rather crude bounds on their averages. In particular, these bounds were proved with simple probabilistic and geometric arguments, so improvements by elementary methods are likely within reach.

Speaker: **Ben Hutz, SLU**

Title: Computational Arithmetic Dynamics

A brief introduction to some computational problems in arithmetic dynamics I am currently thinking about. The emphasis will be on classification type questions, such as identifying invariants that could be used as coordinates for the moduli space.

## AWM Student Chapter Meeting

End of the year celebration.

Monday, May 1, 4pm. Meet in the Ritter Lobby, then carpool to Gelateria on South Grand, arriving around 4:20.

## Master's Thesis Defense

Zach Sarvis, SLU

Tuesday, May 2, 10am, Ritter 229.

Some Analysis Tools for the Study of the Schrödinger Equation

## Master's Thesis Defense

Calin Belean, SLU

Wednesday, May 3, 4pm, Ritter 236.

Moduli spaces of Calabi Yau manifolds: a look at Hermitian and Kahler conditions

## Math Club

Darrin Speegle, SLU

Wednesday, May 3, 3:30-4pm, Ritter Lobby.

Title: Tests for randomness

Description: Suppose that we are given a list of random values. How can we guess whether they were made by a human or by a computer? What kind of statistical tests can we use to inform our guess? We will play around with these kinds of problems and learn some neat tricks!

## Master's Thesis Defense

Jae Hyeong Lee, SLU

Thursday, May 4, 2pm, Ritter 231.

A Study of Bilipschitz Embeddability into Euclidean Spaces

Abstract: In this study, we focus on Assouad's Embedding Theorem, which states that every doubling metric space with its distance raised to the power by some $0 < \varepsilon < 1$ admits a bi-Lipschitz embedding into some Euclidean space. We first show why the upper bound of this inequality is strict by proving that a fractal doubling metric space created by Laakso has no bi-Lipschitz embedding into any Euclidean space. We then apply Assouad's Embedding Thereom on the unit interval in the Euclidean space $\mathbb{R}^2$ to understand the bi-Lipschitz images of doubling spaces that have their distance raised by some power $0 < \varepsilon < 1$.

## Joint CS/Data Science Seminar

Margaret Lund, PhD, Pacific Northwest National Laboratory

Thursday, May 4, 3:45pm, ISE 230.

*Confidence is Key: Quantifying Uncertainty in Fields that Leave No Room for Error*

The National Institute of Standards and Technology (NIST), has extensive guides on how to quantify uncertainty in a measurement model by carefully combining uncertainties in input data with a model’s sensitivities to those inputs. Starting with a high-level overview of NIST uncertainty budgets, we will explore uncertainty quantification (UQ) both in general, and as it applies to machine learning. We will discuss the two commonly cited sources of uncertainty in ML and take a closer look at the seven steps in machine learning procedure to consider how there are uncertainties at every step in the training process. While every field requires precise and accurate UQ, we will discuss two specific research applications in which the results leave no room for error.

## Mathematics and Statistics Department Award Ceremony

Friday, May 5, 4-5:30pm in Lecture Hall 1, with refreshments beforehand.

Featuring the 2023 Case Lecture:

Margaret Lund, PhD, Pacific Northwest National Laboratory

"*Low Hanging Fruit: The value of a mathematician in experimental science"*

A math degree lays the groundwork for a career in any number of fields, from finance and risk modeling to data analytics and experimental science. I’ll discuss my path from majoring in math at Saint Louis University to my current career as a data scientist at Pacific Northwest National Laboratory. Some of my most impactful work has stemmed from identifying simple problems with simple solutions, usually involving nothing more complicated than some vector diagrams, a few partial derivatives, and a little trig. I’ll highlight two of these projects, both related to laser-based data collection techniques for dynamic materials studies (aka blowing stuff up). We will discuss how approaching problems as a mathematician can add immense value to experimental teams that are typically dominated by physicists and engineers.

## Doctoral Thesis Defense

Kathleen Kramer, SLU

Thursday, April 27, 1-3pm, Ritter 334

The Local Smoothing of Reeb Graphs and the Edit Distance for Smoothed Reeb Graphs

## Math Club

Lauren Miller, SLU

Secret codes, how to design and crack them.

Wednesday, April 26, 4pm in the Ritter Lobby

## Master's Thesis Defense

Mary Silverglate, SLU

Title : Cheeger's Inequality: Theory and Applications

Tuesday, April 25, 2:30pm in Ritter 231

Abstract:

Cheeger's inequality is a well-known result from graph theory that states that the conductance of a graph can be bounded from below by the second-smallest eigenvalue of the graph's Laplacian matrix. This master's thesis is a survey paper that presents a comprehensive analysis and proof of Cheeger's inequality in the undirected case and compares various methods for finding analogous inequalities in the directed case. In the first part, we prove Cheeger's inequality for an undirected graph. In the second part, we compare and contrast analogous inequalities for a directed graph using GEANT computer network data. In the last part, we explore applications of Cheeger's inequality in various fields, including Markov chains, image segmentation, and computing networks. This thesis aims to be a useful resource for researchers and students interested in graph theory, spectral theory, and their applications in science.

## Math Club

Bryan Clair, SLU

Title: The new aperiodic monotile

Wednesday, April 19, 3:30-4:30 in Ritter Lobby

The math and CS club is meeting in Ritter Lobby on Wednesday afternoon with tea, soda, snacks, and pizza starting at 3:30. At 4:00 we will start learning and playing with the first ever aperiodic tiling of the plane using a single tile.

A single tile was recently discovered which can be used to tile the plane, but it cannot tile the plane in a periodic way! It is called an Einstein tile which means “one stone” in German. This discovery has been widely discussed among mathematicians, and it has received a lot of press as well: https://www.cnn.com/2023/04/06/world/the-hat-einstein-shape-tile-discovery-scn/index.html

We will learn about tilings of the plane and play around with this new tile.

## Master's Thesis Defense

Emily Twardy, SLU

Title :Supercharacter Theories for Dihedral Groups

Thursday, April 20, 2:30pm in Ritter 236

Abstract:

In Representation Theory, we use character tables to encode information about a group in a compact way, using the irreducible representations of a group and their values for conjugacy classes in that group. However, for some groups, the character table can be quite large and unmanageable, which motivates the introduction of Supercharacter Theories, as first described by Diaconis and Issacs in “Supercharacters and Superclasses for Algebra Groups”. Using Supercharacter Theory, we can condense character tables by adding characters to combine rows, and unioning conjugacy classes to combine columns, while still maintaining information about the group. This talk explores possible supercharacter theories for dihedral groups.

## Doctoral Thesis Defense

Aruna Bandara, SLU

Title : Distinguishing links in the orbifold (A0,k)

Friday, April 21, 10:30am in Ritter 323

## AWM Speaker Series

Dr. Vaishavi Sharma, Ohio State University

Title: P-adic valuations of sequences.

Monday, April 17, 4:10-5:00 in Ritter 249.

## Topology Seminar

Aruna Bandara, SLU

Title: Distinguishing links in the orbifold (A0,k)

Date and time: March 7, Tuesday, from 3:10 pm to 4:00 pm

Venue: RT229

Abstract: The genus one handlebody orbifold (A0,k) is a solid torus with a core of singular points (exceptional points) of order k, where k is a positive integer. A link L in (A0,k) is defined as a submanifold of (A0,k) that is diffeomorphic to a disjoint union of v copies of S^1, with v being a positive integer, and each component of L does not intersect with the set of singular points of (A0,k). The modified Jones polynomial is an invariant for links in (A0,k), developed based on the standard Kauffman brackets and Jones polynomial. In the talk, we will go over its construction and discuss a couple of examples.

## AWM Speaker Series

Monday, March 27, 4:10-5:00 in Ritter 249.

Speaker: T. Christine Stevens

Title: Putting your mathematical ducks in a row.

## AWM Speaker Series

Monday, Feb 27, 2023. Ritter 249, 3-4pm

Speaker: Dr. Shaneeka Favors-Welch, SLU

Title: Math for Justice

## Colloquium

Friday, February 3rd, 4:10-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Speaker: Hugo Panzo, SLU

Title: Old and New on the Hot Spots Conjecture

The Hot Spots conjecture is a famous open problem in the theory of partial differential equations (PDE) that was posed in the 1970's. Loosely speaking, the conjecture claims that starting from any generic initial heat distribution, the location of the temperature extremes of a perfectly insulated and sufficiently regular object will eventually converge to the boundary. In this talk, we survey some old results as well as a new approach to the conjecture known as the *Hot Spots constant*. Along the way, we will explore several connections between PDE and probability theory.

Contact This email address is being protected from spambots. You need JavaScript enabled to view it. for zoom information.

## AWM Chapter Meeting

Monday, February 6rd, 4:10-5:00 in Ritter 249.

Speaker: Mary Silverglate, SLU

Title: So you want to teach STEM?

- What are some potential options to do STEM in education (including, but not limited to, teaching)?
- What do teachers/tutors/other STEM educators realistically make?
- How on earth do you navigate the logistics of teaching STEM without an education degree? (It really does not actually matter what your degree is in if you play your cards right)
- And more!

Please invite any friends who may be interested as well! These topics should also apply to those who are considering education in general, particularly those who do not have an education degree.

As always, snacks, drinks, and friendship will be provided! All genders and majors are welcome!!

## PhD Oral Presentation

Thursday, December 1, 10am-11am in Busch Student Center Room 353.

Speaker: Simon McCreary-Ellis, SLU

Title: Stability of the 'a Trous Algorithm Under Iteration

## Data Science Seminar

Friday, December 2, 11:00-11:50 in Ritter 323

Speaker: Jonathan Sawday, SLU

Title: The Inked/Uninked Spaces Project

The Inked / Uninked Spaces Project is being undertaken by faculty (Jonathan Sawday, Geoff Brewer) and graduate students (Ryan Prewitt and Ahlam Jaber) in SLU's English Department. The group is trying to establish ways in which it might be possible to calculate the ratios of inked and uninked spaces represented in the digitized images of the pages of early modern printed books and documents -- that is texts published in England between c. 1475 and 1700. The team is working with the images preserved in the database known as EEBO (Early English Books Online). This database contains digital facsimiles of the pages of some 147,000 books, amounting to some 34 million pages. We are working at the level of the pixel, which involves designing an algorithm to "read" some ~40 x 10^12 pixels. In our presentation, we hope to demonstrate how such an apparently quixotic undertaking might reveal interesting data about early modern printing practices, about the printers themselves, about genre (e.g. prose, poetry, plays, blank forms, romances, legal texts, theological works, scientific treatises, grammars and catechisms, etc etc.), as well as helping us to better understand the supposed transformation of the renaissance "page" during the 16th and 17th centuries. We would very much value the advice, comments, and (even) help of colleagues in Mathematics and Computer Science in this project.

## Math Club Meeting

Wednesday, November 16, Ritter Lobby. 3:30 snacks, 4:00 start.

Speaker: Emily Twardy

Modular origami is a technique that can be used to build some pretty interesting and impressive models of mathematical objects. In modular origami, you combine multiple units folded from single pieces of paper into more complicated forms. The more units, the larger the shape. The Sonobe unit is a simple example unit from modular origami that is both easy to fold and compatible for constructing a large variety of models. Paper, instruction, and snacks provided!

## Colloquium

Friday, November 18, 11:00-11:50am in Ritter 323.

Speaker: Stefan Steinerberger, University of Washington

Title: A Notion of Curvature on Graphs

Curvature is one of the fundamental ingredients in differential geometry. People are increasingly interested in whether it is possible to think of combinatorial graphs as manifolds and a number of different notions of curvature have been proposed. I will introduce some of the existing ideas (especially combinatorial curvature and the Ollivier-Ricci curvature) then propose a new notion based on a simple and explicit linear system of equations that is easy to compute. This notion satisfies a surprisingly large number of desirable properties – connections to game theory (especially the von Neumann Minimax Theorem) and potential theory will be sketched; simultaneously, there is a certain "magic" element to all of this that is poorly understood and many open problems remain. No prior knowledge of differential geometry is required.

Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for a zoom link if you cannot attend in person.

## Third meeting of the Saint Louis Academy of Mathematical Sciences

Friday, November 18, 6:00-7:00pm in the Pere Marquette Gallery, DuBourg Hall.

Lecture by Stefan Steinerberger, University of Washington

Title: Revisiting the Idea of Boundary

A fundamental recurring principle in mathematics is that among all domains of fixed volume the ball minimizes the surface area of the boundary (and this is one of the reasons why many things in nature are round). It's a fascinating story and we'll show how it took almost 3000 years and several good ideas to make this idea precise. We will then revisit the idea of boundary: classically, it denotes the region between a set and its complement. However, when thinking about social networks or modern data science, there is the question of whether it is possible to define a notion of boundary more abstractly, say, on a combinatorial graph (where there is only the graph and no complement to speak of). If you look at the graph of social connections, for example, is there any sense in which your highly eccentric neighbor who actively avoids people is "on the boundary" as opposed to that other neighbor who is the soul of every party? Such notions do indeed exist and that they lead to rather pretty pictures as well as some tantalizing open problems – as happens frequently in mathematics, looking at things from a new angle will also tell us something new about the classical boundaries in good old Euclidean space.

Dinner served at 7:30pm. Lecture open to the public. RSVP required for dinner.

### AWM Chapter Meeting

Monday, November 7, 4pm Ritter Lobby.

Speaker: Dr. Elodie Pozzi, SLU

Title: From dynamical systems to chaos: An introduction to some fractals

### Colloquium

Friday, November 4, 4:10-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Speaker: Oday Hazaimah, SLU

Title: Gradient Methods in Nonsmooth Optimization

Optimization algorithms are at the core of machine learning models in which gradients play a crucial role for solving nonsmooth convex op- timization problems and their dual variational inequalities. Preliminaries and relations between optimization and inclusion problems are introduced. Classical Gradient-based methods and their modifications find the solution by evaluat- ing the smooth operator twice per iteration. Our goal is to avoid evaluating an extra-gradient step per iteration with strong convergence. In the spirit of cutting-plane methods, the inclusion problem with cocoercive and Lipschitz operators are considered by finding a suitable hyperplane that separates the solution from the current iterate.

Contact This email address is being protected from spambots. You need JavaScript enabled to view it. for zoom information.

### Colloquium

Friday, October 21, 4:10-5:00 in Ritter 323. Refreshments in the Ritter Lobby starting at 3:30.

Speaker: Ravindra Girivaru, UMSL

Title: Matrix factorizations of polynomials

A matrix factorization of a polynomial F is a pair of (square) matrices (A,B) such that their product is F times the identity matrix. After spending some time on preliminaries, I will explain what is known about this question, and what its relevance is to the geometry of hypersurfaces (i.e., the zero locus of polynomials).

### Math Club

Wednesday, September 21.

We are meeting early this week starting at 3pm in Ritter Lobby!

Dr Ben Hutz will be presenting in the Math club about some exciting research opportunities. We will be providing pizza, drinks, and snacks!

Title: **The Arithmetic of Dynamical Systems**

Abstract: I will present the basic definitions in the arithmetic of dynamical systems and present a few problems that would be suitable for student research projects (undergraduate or masters).

### Colloquium

Jason Murphy, Missouri University of Science and Technology

**The scattering map determines the nonlinearity**

We consider several classes of nonlinear Schrödinger equations (NLS) that admit a small-data scattering theory. This refers to the fact that we may construct small global-in-time solutions that scatter backward and forward in time to solutions to the underlying linear equation. This allows us to define the scattering map, which sends the scattered state at t=-\infty to the scattered state at t=+\infty. After discussing the construction of the scattering map, we will consider several scenarios in which one can prove that the scattering map uniquely determines the nonlinearity. Along with reviewing some results due to Strauss and Watanabe, this talk will discuss some joint work with R. Killip and M. Visan.

Friday, September 23, 4:10-5:00pm in Ritter 323 with refreshments at 3:30 in the Ritter Lobby. Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for a zoom link if you cannot attend in person.

### Colloquium

Dr. Özlem Ugurlu, SLU

**Title: Clans, Sects, and Lagrangian Grassmannians**

**Abstract**: Let G = Sp_{2n}(C) and L = GL_{n}(C). The set of cosets of G/L has the structure of an algebraic variety. Furthermore, group B of upper triangular matrices acts on G/L with finitely many orbits. These orbits can be naturally indexed by sets of decorated involutions known as clans, and these indexing sets have bearing combinatorial richness.

I will give an overview of these objects and their relations with other combinatorial objects as well as present some results relating the geometry of Schubert cells (which are B-orbits of a Grassmannian) to the combinatorics of the indexing clan. This is based on joint work with Aram Bingham.

**Date**: Friday, May 6, 4pm Ritter 334 with refreshments at 3:30 in the Ritter Lobby. Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for a zoom link if you cannot attend in person.

### Colloquium

Dr. Hugo Panzo, Technion.

**Spectral upper bound for the torsion function of symmetric stable processes**

Bounds on the product of the principal eigenvalue of the Dirichlet Laplacian and the supremum of the torsion function of Brownian motion that are uniform over a given class of Euclidean domains have been a topic of active research with several improvements and conjectures appearing in the literature recently. We make some progress in the Dirichlet fractional Laplacian and symmetric stable process case by deriving an analogous bound that improves upon the existing result and which captures the correct order of growth in the dimension.

Date: Wednesday, April 27, 11-11:50am Ritter 323.

### Colloquium

Dr. Vignon Oussa, Bridgewater State University.

**HRT conjecture and linear independence of translates on the Heisenberg group**

In this talk, we will establish the relationship between the HRT Conjecture and the linear independence of translation systems on the Heisenberg group. We will show that the HRT Conjecture is equivalent to the conjecture that co-central translates of square-integrable functions on the Heisenberg group are linearly independent. This result affirmatively answers a question asked at the HRT workshop at Saint Louis University in 2016. This is joint work with B. Currey.

Date: Friday, April 29, 11-11:50am Ritter 323.

### 2022 Department Awards Ceremony

Featuring the Case Lecture, by Dr. Vignon Oussa of Bridgewater State University.

**Transcending Struggles:The Accomplishments of African American Mathematicians**

Although African Americans have received only about 1 percent of all PhDs granted in mathematics in the last decade, the Black mathematicians' experience is not just a story of struggles. It is also a marvelous journey of resilience, success, excellence, and achievement. Despite the perpetual challenges that African American mathematicians had to surmount, they have immensely contributed to the subject of Mathematics. In this talk, we will be exploring the accomplishments and struggles of African American mathematicians and how these experiences have shaped the scientific community.

Date: Friday, April 29 from 4-5:30 in Lee Lecture Hall with refreshments beforehand.

### Doctoral Thesis Defense

Sarah Aljohani, SLU.

Date: Thursday, March 3. Public portion from 9-10am in Ritter 231.

**Title**: Generalizations of Prime ideals for Leavitt path algebras

**Abstract**:

Leavitt path algebras are algebraic analogues of graph C∗-algebras and are also natural generalizations of algebras without invariant basis number constructed by William Leavitt. Although Leavitt path algebras are non- commutative, their ideal theory is quite similar to that of commutative rings. Several variations of prime ideals such as irreducible ideals, strongly irreducible ideals, strongly prime ideals and insulated prime ideals have been studied in literature by commutative ring-theorists. In this dissertation these notation have been explored in the context of Leavitt path algebras. We characterize those Leavitt path algebras whose each ideal admits factorization in terms of ideals of these types. Leavitt path algebras whose each ideal is one of these special type of ideals is also characterized and we give necessary and sufficient conditions under which a proper ideal of a Leavitt path algebras is a product as well as an intersection of finitely many of these special ideals. Some of this work has also been extended to the case of Leavitt path algebras with coefficients in commutative rings ( not necessary fields).

### Graduate Student Seminar

Katie Kramer, SLU.

Thursday, Feb. 17, 2022, 3-4pm in Ritter 334. A zoom livestream will be provided, write to This email address is being protected from spambots. You need JavaScript enabled to view it. for details.

**Title**: Reeb Graphs

**Abstract**:

Reeb graphs, originally studied in Morse theory, are one tool used to help examine topological and geometric information about shapes. The Reeb graph can give topological and geometric information about our shape which helps yield local and global information about the shape. Reeb graphs are often utilized in computational topology as well as topological data analysis (TDA). This seminar will focus on understanding Reeb graphs and specifically understanding two different distances (interleaving distance and Reeb graph edit distance) as ways to compare Reeb graphs.

### Colloquium

Darrin Speegle, SLU.

Friday, Dec 3, 2021, from 4:00 p.m. to 5:00 p.m. in Ritter 334. A zoom livestream will be provided, write to This email address is being protected from spambots. You need JavaScript enabled to view it. for details.

**Title**:

Simultaneous dilation and translation tilings of R^n

**Abstract**:

Let A be an invertible, n by n matrix, and let G be a lattice in R^n. A set W is an (A, G) wavelet set if the following two collections of sets are tilings of R^{n}: {A^{j}(W): j in Z} and {W + g, g in G}.

In my thesis in 1997, I stated that "A natural question would be to characterize all matrix-lattice pairs for which there are wavelet sets." In this talk, I provide such a characterization. I will start with some examples and early results, and then relate the problem to studying the limit behavior of the cardinality of A^{j}(B) \cap G (where B is the unit ball in R^{n}), which leads to the characterization.

This talk is based on joint work with Marcin Bownik.

**AWM Talk**

Ozlem Ugurlu, SLU. Monday, November 15th, 2021 from 4-5pm in Ritter 202.

Dr. Ugurlu will be leading us through the basics of a branch of mathematics called combinatorics, mathematics that's all about the beauty of counting. She'll be going over some historical examples as well some fun problems. All are welcome, come enjoy some snacks, have a fun time, and meet some fun people.

**AWM Talk**

Stacey Harris, SLU. Monday, October 18th, 2021 from 4-5pm in Ritter 202.

Title: How I Came to the Boundary of Spacetime

This is the first in a planned series of talks given by the women of the math department, in which they describe how they have gotten to where they are today, as well as an overview of their research area. Suitable for undergraduates of all genders.

### Master's Thesis Defense

Asma Zangana, SLU. Thursday, May 6th, 2021, from 1:30 p.m. to 3:30 p.m. via Zoom. Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for zoom information.

**Title**:

Computation of Minimal and Formal Periodic Points for Dynamical Systems in Projective Space.

**Abstract**:

Computing minimal and formal periodic points of a given period in one-dimensional dynamics is a straightforward polynomial division. However, computing minimal and formal periodic points of a given period of a system of multivariable polynomial equations in higher-dimensional dynamics has not been done. Hence, the focus of this thesis is to compute minimal and formal periodic points for dynamical systems in projective space using saturation and deformation.

Computing minimal periodic points of a given period using saturation of ideals proves to be the effective method to compute all the minimal periodic points of a given period. However, the multiplicity information is lost under saturation due to the geometric nature of saturation. Computing formal periodic points for a given period using saturation of ideals alone proves to not produce all the formal periodic points for a given period due to the geometric nature of saturation. Thus, using deformation first by adding a parameter to the coordinates of the dynamical system and then applying saturation of ideals is the effective method to produce all the formal periodic points of a given period with the correct multiplicity. All computations have been done using Sage, and the Appendix provides the complete Sage code that has been used for each example in this thesis.

### Master's Thesis Defense

Tuesday, July 28, 2020. Public portion from 9-10am. Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for an invitation to attend this Zoom meeting.

Christian Verghese, SLU

A Survey of Deterministic and Probabilistic Methods in Compressive Sensing.

**Abstract:**

Compressive sensing is an area of mathematics concerning the recovery of sparse signals from a small number of linear measurements. This recovery problem naturally involves an underdetermined system of linear equations. The main goal in solving this system is to design a collection of measurements that distinguishes any pair of sparse vectors and permits efficient recovery. One significant finding in compressive sensing is that the number of measurements required for successful recovery depends on the sparsity of the signal considered. A well-known condition featured in the literature is the restricted isometry property, which is a sufficient condition for sparse recovery. There is no explicit method for constructing arbitrarily large measurement matrices with the restricted isometry property; however, families of random matrices have been shown to satisfy this property with high probability.

This thesis is expository in nature and surveys these breakthroughs in compressive sensing. The first part analyzes two sufficient conditions on the measurement matrix for successful reconstruction of a sparse signal. In particular, it is shown that a measurement matrix with sufficiently low restricted isometry property satisfies the robust null space property, which guarantees sparse vector recovery. The second part of the thesis explores the construction of suitable measurement matrices by employing probabilistic methods. The focus here is to illustrate that suitable random matrices with a relatively small number of measurements lead to sparse recovery with high probability.

### PhD Defense

Monday, July 27, 2020. Public portion from 12-1pm.

Seth Arnold, SLU

Homotopy Types of Quotients of T2 × S3 by Free Involutions with Torsionfree Fundamental Group

### Master's Thesis Defense

Friday, July 24. Public portion from 2-3pm. Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for an invitation to attend this Zoom meeting.

Arnab Dey Sarkar, SLU

Cremona Monomial Maps

**Abstract:** In 1930-1990, a presentation for the Cremona group is obtained by Masayoshi Nagata, Vyacheslav Vladimirovich Shokurov, Aleksandr Danilovich Aleksandrov, Vladimir Ivanovich Danilov for any n. A key problem is the classification of finite subgroups. This has now been proved for Cr(2), but it is still unknown if every finite group is a subgroup of Cr(4). The study of the iteration of a birational map begins to be studied. Here I have interpreted the Cremona monomial maps in terms of log matrix and then find out how many such cremona monomial maps are there of degree 1 to 20 and then we discussed the maps that commute with quadratic involution. In this thesis we will be working on classification of Cr(3) as well.

**PhD Defense**

Chirasree Chatterjee

Friday July 3 at 12noon via Zoom. Please write to Stacey Harris This email address is being protected from spambots. You need JavaScript enabled to view it. for the link.

Title: Short Time Existence and Uniqueness of Ricci Flow in Standard Static Spacetimes

Abstract: Ricci flow exists and is unique for a short time on compact Riemannian manifolds. The proof of this claim involves a trick called the DeTurck trick used to transform the non-parabolic Ricci flow equation to a parabolic equation which therefore admits a short time unique solution. This solution when pulled back via an appropriate family of diffeomorphisms results in a solution to the original Ricci flow. In this thesis we replicate the aforementioned technique on the class of standard static spacetimes with a closed and compact spatial component to prove the uniqueness and existence of Ricci flow on such manifolds for a short time.

### Doctoral Thesis Defense

Tuesday, May 12. Public portion from 12-1pm. Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for an invitation to attend this Zoom meeting.

Katie Radler, SLU

"Ideals of Leavitt path algebras and their supersymmetric analogues"

### Master's Thesis Defense

Friday, April 17. Public portion from 2-3pm. Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for an invitation to attend this Zoom meeting.

Sadita Salihovic, SLU

"The Qualitative, Quantitative, and Topological Data Analysis of Implementing a Semi-Flipped Classroom Approach in an Introductory Statistics Course Tailored Towards Health Care Students"

### Colloquium

Friday, March 6 from 4-5pm in RH 242 with refreshments at 3:30 in the RH Lobby.

Peter Pivovarov, University of Missouri

Title: Convexity and Stochastic Isoperimetry

Abstract: Isoperimetric principles govern fundamental relationships between shapes and their size. A protypical example is the isoperimetric inequality which dictates the maximum area of sets of a given perimeter. While such a principle holds well beyond the class of convex sets, more can be said when convexity is present. In particular, there is often an accompanying *local stochastic dominance*. This gives rise to stronger inequalities which give back the classical versions via laws of large numbers. I will illustrate this theme via several examples that sit at the meeting place of geometric probability, convex geometry and analysis. The talk will be expository, with no special background assumed.

### Colloquium

Friday, Feb 28 from 4-5pm in RH 242 with refreshements at 3:30 in the RH Lobby.

Hannah Schreiber - SLU Computer Science

Title: Introduction to standard and non-standard Persistent Homology

Abstract: Persistent homology enables the analysis of evolving topological properties of general data sets through different scales. The standard case is persistent homology of filtrations, a sequence of nested complexes. The persistent homology is represented by a barcode consisting of the birth and death times of the different cycle classes evolving through the growing complex. The talk will aim to introduce those notions for filtrations, but also for more general inputs as towers and zigzag filtrations and give an overview of the current state of the art.

### PhD Oral Exam

Tuesday, Feb 25 from 2-3pm in Ritter 334

Rehab Alharbi

Title: Smoothing Functor on Reeb Graphs

### Colloquium

Friday, Feb 14 from 4-5pm in RH 242 with refreshements at 3:30 in the RH Lobby.

Dan Freeman, SLU

Title: Stable phase retrieval for infinite-dimensional subspaces of L^{2}R.

Abstract: The problem of phase retrieval for a set of functions H can be thought of as being able to identify a function f ∈ H or −f ∈ H from the absolute value |f|. Phase retrieval for a set of functions is called stable if when |f| and |g| are close then f is propor- tionally close to g or −g. That is, we say that a set H ⊆ L2(R) does stable phase retrieval if there exists a constant C > 0 so that min(||f − g||, ||f + g||) ≤ C|| |f| − |g| || for all f, g ∈ H.

It is known that phase retrieval for finite dimensional spaces is always stable. On the other hand, phase retrieval for infinite dimensional spaces using a frame or a continuous frame is always unstable. We prove that there exist infinite dimensional subspaces of L2(R) which do stable phase retrieval. This is joint work with Robert Calderbank, Ingrid Daubechies, and Nikki Freeman.

### Math/CS Club

Wednesday, Feb 12 in RH Lobby at 4:00pm with refreshements at 3:30.

Lauren Miller is leading the club this week in making Sierpinski’s “heart” valentines cards. Fall in love with the only surface that has only one side and one boundary, and make origami hearts! Lauren will talk a little bit about the relation between math and paper folding, as well as share some information from when she visited the international origami museum. After demonstrating the Möbius strip activity, we will have stations with paper, examples, and instructions so people can craft as they wish.

### Math/CS Club

This week in the Math-CS club we will play with some combinatorial puzzles made by Barry Cipra. Each of the puzzles deals with arranging square tiles to make a certain pattern. We will also play the tile laying game Tsuro. The club meets Wednesday 4-5pm in Ritter Lobby.

Before the club is the **Math-stat-CS departmental tea at 3:30 in Ritter Lobby**. We will have tea, coffee, and food. Faculty, grad students, and undergrad students are all welcome.

### Algebra Seminar

Katie Radler, SLU

Tuesday, 1/28 from 11-12 in Ritter 242.

Title: Ideals in Leavitt path algebras and Leavitt path superalgebras.

Abstract: In this talk, I will do an overview of Leavitt path algebras and Leavitt path superalgebras. I will then talk about ideals in Leavitt path algebras and recent work done about ideals in Leavitt path algebras. I will finish with the most current work done in ideals of Leavitt path superalgebras.

### PhD Oral Exam

Sarah Aljohani, SLU

Thursday Dec-5th , from 9:10 am, in room 314 .

Title: VARIATIONS OF PRIMENESS AND FACTORIZATION OF IDEALS IN LEAVITT PATH ALGEBRAS.

Abstract: Describe strongly irreducible ideals, strongly prime ideals and insulated prime ideals of Leavitt path algebras. characterize under which conditions a proper ideal of a Leavitt path algebra is a product of finitely many ideals of these types.

### Colloquium

Alexander Garver, University of Michigan

Friday, December 6 at 4:00pm in Ritter 242 with refreshments beforehand in the Ritter Hall Lobby.

Title: Reverse plane partitions via quiver representations

Abstract: A reverse plane partition is an order reversing map from a poset to the nonnegative integers. We study reverse plane partitions on the so-called minuscule posets. A minuscule poset is defined by choosing a Dynkin diagram and a minuscule vertex of the Dynkin diagram. We show that there is a bijection between reverse plane partitions on a minuscule poset and representations of a Dynkin quiver of the corresponding type all of whose indecomposable summands are supported on the minuscule vertex. I will not assume any prior knowledge of quiver representations. This is joint work with Rebecca Patrias and Hugh Thomas.

### PhD Defense

^{2}(G) and is an isometry, we call this a continuous wavelet transform and that psi is a continuous wavelet or admissible for tau. We will give a general Calderon condition for when such admissible vectors exist given some assumptions on N. Then, we will explicitly construct and decompose the quasi-regular representation on the class of odd degree oscillator groups and use this to show that G admits no admissible vectors but the dilated group G

_{d}does.

### Sage Days 104: Arithmetic Dynamics

November 17-20. BSC Room 254.

This 4-day workshop includes a combination of mathematical talks, Sage tutorials, and Sage development. The main goal is to promote and improve the dynamical systems functionality in Sage and to expand the scope of the database of dynamical systems. Users new to Sage and Sage development are welcome. There is no initial knowledge needed, everyone is welcome whether they are new Sage learners or Sage expert. We believe in diversity in backgrounds and experiences.

For details, visit the workshop website at: https://wiki.sagemath.org/days104

### Master's Thesis Defense

Nick Simone, SLU

A Score Minimizing Vertex Partitioning Algorithm using Simulated Annealing

Thursday, November 21 at 9:30am in Ritter 334.

### Colloquium

Courtney Paquette, Google Brain, Montreal

Friday, November 15 at 4:00pm in Ritter 242 with refreshments beforehand in the Ritter Hall Lobby.

Title: Algorithms for stochastic nonconvex and nonsmooth optimization

Abstract:

Machine learning has introduced new optimization challenges with its use of nonconvex losses, noisy gradients, and statistical assumptions. While convergence guarantees in the deterministic, convex settings are well-documented, algorithms for solving large-scale nonsmooth and nonconvex problems remain in their infancy.

I will begin by isolating a class of nonsmooth and nonconvex functions that can be used to model a variety of statistical and signal processing tasks. Standard statistical assumptions on such inverse problems often endow the optimization formulation with an appealing regularity condition: the objective grows sharply away from the solution set. We show that under such regularity, a variety of simple algorithms converge rapidly when initialized within constant relative error of the optimal solution. We illustrate the theory and algorithms on the real phase retrieval problem, and survey a number of other applications, including blind deconvolution and covariance matrix estimation.

One of the main advantages of smooth optimization over its nonsmooth counterpart is the potential to use a line-search for improved numerical performance. A long-standing open question is to design a line-search procedure in the stochastic setting. In the second part of the talk, I will present a practical line-search method for smooth stochastic optimization that has rigorous convergence guarantees and requires only knowable quantities for implementation.

### Colloquium

Khazhak Navoyan, University of Mississippi Oxford

Friday, November 1 at 4:00pm in Ritter 242 with refreshments beforehand in the Ritter Hall Lobby.

Title: **The positive Schur property on spaces of regular multilinear operators**

Abstract: In this paper we give necessary and sufficient conditions for the space of regular multilinear operators from the product of Banach lattices to a Dedekind complete Banach lattice to have the positive Schur property. We also characterize the positive Schur property on the positive projective n-fold tensor product of Banach lattices, n ε N, and on its dual.

### Algebra Seminar

Katie Radler and Sarah Aljohani, SLU graduate students

A weekly series of talks, Tuesday, September 24 - Tuesday, October 15 at 11:00am in Ritter 229.

**Variations of prime ideals and factorization of ideals in Leavitt path algebras**

### Colloquium

Salman Parsa, SLU

Friday, October 11 at 4:00pm in Ritter 242 with refreshments beforehand in the Ritter Hall Lobby.

**Obstructions to embedding the join of two simplicial complexes in Euclidean spaces**

The problem of embedding (i.e., mapping continuously and injectively) a simplicial complex of dimension d into a Euclidean space of dimension 2d is a generalization of the problem of drawing a graph on a plane. When d>2, there exists a complete homological obstruction for deciding the embeddability of a complex into 2d space. This is called the van Kampen obstruction. We discuss this concept and state and explain new results that enable us to decide the vanishing of the van Kampen obstruction of the join of two complexes based on the obstruction classes of the factors.

### Colloquium

Charles Burnette, SLU

Friday, September 20 at 4:00pm in Ritter 242 with refreshments beforehand in the Ritter Hall Lobby.

**Title: Involution factorizations of Ewens random permutations**

Abstract: An involution is a permutation that is its own inverse. Given a permutation σ of [n], let invol_{n}(σ) denote the number of ways to express σ as a composition of two involutions of [n]. The random variables invol_{n} are asymptotically lognormal when the symmetric groups S_{n} are each equipped with Ewens Sampling Formula probability measures of some fixed positive parameter θ. In this talk, I will summarize what is already known and explain new results about the previously determined limiting distribution of invol_{n} for uniform random permutations, i.e. the specific case of θ = 1.

### PhD Defense: Christopher Halverson

Gradient Young Measures and Maps of Exponentially Integrable Distortion

Abstract: We aim to extend the relationship established by Astala and Faraco between functions of bounded distortion and gradient Young measures to the more general setting of maps of exponentially integrable distortion. We will do this using techniques derived from singular operator theory.

Ritter Hall 229 at 10am on July 29th

### Departmental Awards Ceremony

Friday, April 26 in Lee Lecture Hall. Refreshments at 4:00pm. Ceremony begins at 4:20pm.

Featuring the 2019 Case Lecture by Dr. Liberty Vittert, Washington University in St. Louis

**How to win the lottery and get away with murder**

Abstract: Data, numbers statistics are coming at us like a hurricane, it can be completely overwhelming. This influx of data means that government, media, businesses, advertisers, and even scientists will be using data and numbers to sway your opinion, rightly and wrongly. With enormous amounts of information we run the risk of misinformation and even more worrisome disinformation. Using real-life examples and good old common sense, we are going to learn what questions we should be asking of data in order to spot the lies, damned lies, and statistics (with a little fake news thrown in there for good measure).

### Colloquium

K. M. Rangaswamy, University of Colorado, Colorado Springs

*Wednesday*, April 3, at 4:10pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

Title:** Are Leavitt path algebras really commutative algebras in non-commutative clothing?**

Abstract: Leavitt path algebras of directed graphs over a field are algebraic analogues of graph C*-algebras of operators on Hilbert spaces. This talk is a report on some of the recent investigations illustrating two essential features of these algebras. The first makes the Leavitt path algebras really useful tools in constructing examples of rings of various types. The second is about the ideal lattice of Leavitt path algebras, which seems to posess similarities with commutative rings. Various graphical constructions will illustrate these conclusions.

### Algebra Seminar

Steve Szabo, Eastern Kentucky University

Thursday, April 4, 10:00-10:50am in Ritter 225

Title: **Minimal Reversible Nonsymmetric Rings and other Related Minimal Rings**

Abstract:

In a paper by Marks on the taxonomy of 2-primal rings, examples of various types of rings that are related to 2-primal rings such as reduced, symmetric, duo, reversible and PS I were given in order to show that the ring class inclusions were strict. In this talk, this taxonomy is refined to include NI, abelian and reflexive rings. Then minimal examples of all ring types possible are provided. In particular, it is shown that the F_2 algebra over Q_8 is a minimal reversible nonsymmetric ring answering a question by Marks on such rings. Finally, connections to minimal abelian reflexive nonsemicommutative rings are also discussed.

### Colloquium

William Yslas Vélez, University of Arizona

Friday, April 5, at 4:10pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**Increasing the mathematical content of the undergraduate curriculum for all students. Good for the student. Good for the university.**

Abstract: In the late 1980’s I began my efforts to increase the success rate of minorities in first semester calculus. These minority students came from all majors, though most were in engineering. The interventions that I devised were very time consuming and as the number of minority students increased, I could not manage that kind of effort. I developed my Calculus Minority Advising Program in an effort to meet with scores of minority students each semester. This program consists of a twenty-minute meeting with each student at the beginning of each semester. The meetings with the students eventually transformed my own attitude about the importance of mathematics in their undergraduate curriculum. It sloooowly dawned on me. The more mathematics a student took, the more opportunities were available to that student.

I took over the position of Associate Head for Undergraduate Affairs in the department in 2003. My work with minority students provided me with the tools to accept the new challenge of encouraging students to take more mathematics and to think about adding the math major or math minor to their program of study.

One can see the impact of these efforts across our university. With 600 mathematics majors and 700 mathematics minors, oftentimes the outstanding graduating senior in another department also has a mathematics major or minor. Our mathematics majors who also have another major are being accepted into graduate programs at the most elite universities in their other major.

The work that I do is focused on helping students reach their goals. Given the increasingly important role that mathematics now plays in society, taking more mathematics is essential. Mathematics departments need to communicate this to their students.

### Doctoral Dissertation Defense

James Mixco, Saint Louis University

Thursday, April 11, 10:00am-12:00pm (the first hour is public), in Ritter 202

**Supersymmetric Cluster Algebras and Their Quantum Deformations**

Abstract: Fomin and Zelevinsky introduced cluster algebras in 2001. A cluster algebra is a commutative ring generated by variables obtained by an iterative combinatorial process called mutation. From the time of their inception, cluster algebras have been found to have applications to several branches of mathematics and physics. These include algebraic geometry, Poisson geometry, Teichmuller space theory, combinatorics, and analysis.

More recently, an approach towards defining cluster algebras with Grassmann variables has been proposed by Ovsienko. This attempt has quite a few limitations. Here, we give an approach to supersymmetric cluster algebras independent of Ovsienko and provide some new interesting geometric examples. This work is largely based on the work done by Li, Mixco, Ransingh, and Srivastava. In addition to what is done by Li, Mixco, Ransingh, and Srivastava, we expand the theory of cluster superalgebras by proving theorems analogous to classical cluster algebra theorems. Beyond that, we extend our notion of cluster superalgebras to quantum cluster algebras.

### Colloquium

Mihai Ciucu, Indiana University

Friday, April 12, at 4:10pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

**The interaction of gaps with the boundary in dimer systems --- a heat flow conjecture**

Abstract: We consider a triangular gap of side two in a 90 degree angle on the triangular lattice with mixed boundary conditions: a constrained, zig-zag boundary along one side, and a free lattice line boundary along the other. We study the interaction of the gap with the corner as the rest of the angle is completely filled with lozenges. We show that the resulting correlation is governed by the product of the distances between the gap and its three images in the sides of the angle. This, together with a few other results we worked out previously, provides evidence for a unified way of understanding the interaction of gaps with the boundary under mixed boundary conditions, which we present as a conjecture. Our conjecture is phrased in terms of the steady state heat flow problem in a uniform block of material in which there are a finite number of heat sources and sinks. This new physical analogy is equivalent in the bulk to the electrostatic analogy we developed in previous work, but arises as the correct one for the correlation with the boundary.

The starting point for our analysis is an exact formula we prove for the number of lozenge tilings of certain trapezoidal regions with mixed boundary conditions, which is equivalent to a new, multi-parameter generalization of a classical plane partition enumeration problem (that of enumerating symmetric, self-complementary plane partitions).

### 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.