# Math Calendar

### Upcoming Events

## NUMBER THEORY- A modular framework of functions of Knopp – Location- SC 1310

Andreas Mono – Vanderbilt University

This talk presents the construction of a modular completion of a function introduced by Knopp $30$ years ago in his paper \textit{Modular integrals and their Mellin transforms}. His function is closely related to a term by term lift of Zagier’s influential $f_{k,D}$ function under the Bol operator. We begin with a motivation of the topic, and summarize some background briefly. Afterwards, we outline our constructions, and discuss their naturality. We connect our result to the more recently introduced concept of locally harmonic Maa{\ss} forms by Bringmann, Kane, and Kohnen about $10$ years ago. In addition to that, we present connections of our results to some earlier work on hyperbolic Eisenstein series and their local modular completions. The first part is joint work with Kathrin Bringmann.

## COMPUTATIONAL ANALYSIS SEMINAR- One-box Conditions for Carleson Measures- Location- SC 1308

Prof. Javad Mashreghi – Laval University, Quebec, Canada

We show that a finite measure $\mu$ on the unit disk is a Carleson measure for the Dirichlet space if it satisfies the Carleson one-box condition $\mu(S(I)) = O(\phi(|I|))$, where $\phi:(0,\2\pi) \to (0,\infty)$ is an increasing function such that $\int_{0}^{2\pi} \phi(x)/x \, dx < \infty$. We also show that the integral condition on $\phi$ is sharp.

## Topology & Group Theory Seminar

## Topology and Group Theory-Representation growth of property (T) groups and Voiculescu’s entropy theory- Location- SC 1308

Srivatsav Kunnawalkam Elayavalli – UCSD

I will describe a connection between an old difficult question of Wigderson from the 60’s on representation growth of countable property (T) groups and 1-bounded entropy which is a modern invariant of von Neumann algebras introduced by Jung and Hayes. It seems to be a win-win situation: either there is a negative solution to Wigderson’s question or there is a property (T) von Neumann algebra with 1-bounded entropy strictly between 0 and infinity, which would be a very powerful tool in von Neumann algebra theory that would bring new light into old open problems in II1-factor theory. Moreover, under the assumption of flexible Hilbert-Schmidt stability, these two problems are shown to be the same. The talk will be accessible to group theorists, I will not get into von Neumann algebra theory. This is based on joint work with Hayes and Jekel, and Hayes and Thom.

## Professional Learning Community for New Math Instructors and TA’s – Location SC 1404

Understanding Student Perceptions Through Student Evaluations.

Understanding Student Perceptions Through Student Evaluations.

## Colloquium

## Mixing Surfaces, Algebra, and Geometry and Dynamical Sampling and Frames – Location- SC 5211

Dan Margalit- Department of Mathematics, Chairman and Akram Aldroubi- Department of Mathematics Stevenson Professor

This year, along with our invited guests from other universities, we plan to invite several fantastic speakers from our own faculty to give short colloquium talks. This Thursday we will have two speakers who will each give a 15-minute talk followed by 10 minutes of questions and discussion. We look forward to hearing from many of our colleagues in the next few months! We hope to see all of you on Thursday!

## PDE Seminar- Global solutions of vortex front problems for quasi-geostrophic shallow-water equation- Location- Zoom

Qingtian Zhang, West Virginia University. Zoom link: https://vanderbilt.zoom.us/j/96817406216

In this talk, I will introduce the vortex front problem for quasi-geostrophic shallow water equation, which is also known as Hasegawa-Mima equation in plasma science. The contour dynamic equation of the vortex front will be derived, which is a nonlocal, nonlinear dispersive equation. The existence of global solutions will be proved when the initial data is small. This is a joint work with Fangchi Yan.

## subfactor Seminar

## SUBFACTOR SEMINAR: Structure of free group factors. Location-SC 1432

Srivatsav Kunnawalkam Elayavalli, UC San Diego

I will speak about joint work with Hayes and Jekel where we show various new structural properties of the (more generally interpolated) free group factors, that strikingly generalize most of the currently known results. Some of these include the resolution of the coarseness conjecture, a vastly general strong solidity theorem, structure of ultraproduct embeddings of subalgebras, among others. The proofs use the Hayes’ random matrix approach of the Peterson Thom conjecture, combined with abstract 1-bounded entropy permanence properties.

## Topology & Group Theory Seminar

## Topology and Group Theory-Nielsen realization for 3-manifolds- Location- SC 1308

Bena Tshishiku Brown University

Given a manifold M, the Nielsen realization problem asks when a finite subgroup of the mapping class group Mod(M) lifts to the diffeomorphism group Diff(M) under the natural projection Diff(M) → Mod(M). In this talk, we consider the Nielsen realization problem for 3-manifolds and give a solution for subgroups of Mod(M) generated by sphere twists. This is joint work with Lei Chen.

## PDE Seminar- Global existence and decay of small solutions for quasi-linear second-order uniformly dissipative hyperbolic-hyperbolic systems. SC 1431

Matthias Sroczinski, Konstanz University, Germany. Zoom link: https://vanderbilt.zoom.us/j/92410579521

Abstract: We consider quasilinear systems of partial differential equations consisting of two hyperbolic operators interacting dissipatively. Global-in-time existence and asymptotic stability of strong solutions to the Cauchy problem close to homogeneous reference states are shown in space dimensions larger or equal to 3. The dissipation is characterized by algebraic conditions, previously developed by Freistühler and the speaker, equivalent to the uniform decay of all Fourier modes at the reference state. As a main technical tool para-differential operators are used. The result applies to recent formulations for the relativistic dynamics of viscous, heat-conductive fluids such as notably that of Bemfica, Disconzi and Noronha (2018.).

## SUBFACTOR SEMINAR- An index for quantum cellular automata on fusion spin chains- Location- SC 1432

Junhwi Lim, Vanderbilt University

The index for 1D quantum cellular automata (QCA) was introduced to measure the flow of the information by Gross, Nesme, Vogts, and Werner. Interpreting the index as the ratio of the Jones index for subfactors leads to a generalization of the index defined for QCA on more general abstract spin chains. These include fusion spin chains, which arise as the local operators invariant under a global (categorical/MPO) symmetry, and as the boundary operators on 2D topologically ordered spin systems. We introduce our generalization of index and show that it is a complete invariant for the group of QCA modulo finite depth circuits for the fusion spin chains built from the fusion category Fib. This talk is based on a joint work with Corey Jones.

## NUMBER THEORY SEMINAR- Asymptotics for nonmodular infinite products and the Seo-Yee conjecture;Location: Zoom

Speaker: Shane Chern (Dalhousie University -Zoom Link

https://vanderbilt.zoom.us/j/93816792027?pwd=Qmd1eWRkL3l2YVNOdUM5OEpaY2FJZz09

In this talk, I will present my recent work on the asymptotics for a generic family of nonmodular infinite products near

an arbitrary root of unity. More precisely, our attention is focused on infinite products of the form $1/(q^a;q^M)_\infty$ where $M$ is a positive integer and $a$ is any of $1, 2, \ldots, M$. Such asymptotic expansions will be utilized to prove a conjecture of Seunghyun Seo and Ae Ja Yee, up to a finite check. The Seo-Yee Conjecture, asserting

that the series expansion of a certain infinite product has nonnegative coefficients, is equivalent to the Coll-Mayers-Mayers Conjecture on the index statistic for seaweed algebras.

## Topology & Group Theory Seminar

## Topology and Group Theory- Title: TBA- Location- SC 1308

Denis Osin – Vanderbilt

Let Gn denote the space of n-generated marked groups. The natural action of the group Aut(Fn) on Gn gives rise to a topological dynamical system, which is of fundamental importance to the study of the isomorphism relation on Gn. In my talk, I will discuss some natural problems concerning the existence of invariant measures for this system and its subsystems. In particular, I will answer two questions asked by Grigorchuk and Kaimanovich. Perhaps surprisingly, the main tools used in this work are a group theoretic version of Dehn filling in 3-manifolds and infinitary model theory.

## SUBFACTOR SEMINAR- Title- TBA- Zoom Talk

Pieter Naaijkens, Cardiff University

Abstract-TBA

## PDE Seminar- Title- On the impact of spatially heterogeneous human behavioral factors on 2D dynamics of infectious diseases. SC- 1431

Chuntian Wang, The University of Alabama

Abstract: It is well observed that human natural and social behavior have non-negligible impacts on spread of contagious disease. For example, large scaling gathering and high level of mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may reduce infectious contacts. In order to understand spatial characteristics of epidemic outbreaks like clustering, we formulate a stochastic-statistical epidemic environment-human-interaction dynamic system, which will be called as SEEDS. In particular, a 2D agent-based biased-random-walk model with SEAIHR compartments set on a two-dimensional lattice is constructed. Two environment variables are taken into consideration to capture human natural and social behavioral factors, including population crowding effects, and public preventive measures in the presence of contagious transmissions. These two variables are assumed to guide and bias agent movement in a combined way. Numerical investigations imply that controlling mass mobility or promoting disease awareness can impede a global-scale spatial population aggregation to form, and consequently suppress disease outbreaks. Importance of coordinated public-health interventions and public compliance to these measures are explicitly demonstrated. A mechanistic interpretation of spatial geometric traits in progression of epidemic transmissions is provided through these findings, which may be useful for quantitative evaluations of.

## SUBFACTOR SEMINAR-Title TBA- Location- SC 1432

Sayan Das, Embry-Riddle Aeronautical University

Abstract- TBA

## Topology & Group Theory Seminar

## Geometric Boundary of Groups – Location: SC 1308

Yulan Qing – University of Toronto

Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk, we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk. The sublinearly Morse boundary is a subset of all directions with desired properties. In the second half we will truly consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries embed. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.