**Seminars and Colloquiums**

for the week of November 18, 2019

for the week of November 18, 2019

*SPEAKERS*

Monday

Louis Gross, UTK**
**Larry Rolen, Vanderbilt University

**Tuesday**

Jerzy Dydak, UTK

**Wednesday**

Shuler Hopkins, UTK

Tricia Phillips, UTK

**Thursday**

Timothy Robertson, UTK

Robin Baidya, UTK

Ephy Love, UTK

Julian Scheuer, Columbia University

** Tea Time** -

3:00 pm – 3:30 pm

Monday, Tuesday, & Wednesday

Room: Ayres 401

Hosted by: Delong Li

Topics: How to write a cover letter; What to include/not include on a resume or CV for an academic/industry position; Weekly check-in

**Monday, Nov. 11**

**
MATH BIOLOGY
**Title: More on Complexity Theory

Speaker: Louis Gross

Time: 10:10-11

Room: Claxton 105

** ALGEBRA SEMINAR
**TITLE: Periodicities for Taylor coefficients of half-integral weight modular forms

SPEAKER: Larry Rolen, Vanderbilt University

TIME: 3:35 PM

ROOM: Ayres 114

ABSTRACT: Congruences of Fourier coefficients of modular forms have long been an object of central study. By comparison, the arithmetic of other expansions of modular forms, in particular Taylor expansions around points in the upper-half plane, has been much less studied. Recently, Romik made a conjecture about the periodicity of coefficients around $\tau=i$ of the classical Jacobi theta function. Here, in joint work with Michael Mertens and Pavel Guerzhoy, we prove this conjecture and generalize the phenomenon observed by Romik to a general class of modular forms of half-integral weight.

** Tuesday, 11/19**

**TOPOLOGY/GEOMETRY SEMINAR**

TITLE: Visual boundary of geodesic spaces

SPEAKER: Jerzy Dydak, UTK

TIME: 11:10-12:25 PM

ROOM: Ayres 114

ABSTRACT: Visual boundary of CAT(0) spaces is usually defined as the space of geodesic rays with the cone topology. I will define the visual boundary of a larger class of proper geodesic spaces. It consists of equivalence classes of sequences $x_n$ diverging to infinity such that the geodesics $[p,x_n]$ converge point-wise to a geodesic ray. Since we do not want dependence on the base-point $p$, the natural axiom (which can be verified for CAT(0) spaces) is that convergence of geodesics $[p,x_n]$ implies convergence of $[q,x_n]$ for any $q$. The natural topology on such defined boundary is that of point-wise convergence. It turns out the boundary is compact metrizable and $X$ union the boundary is a compactification of $X$.

**Wednesday, Nov. 20**

**ANALYSIS SEMINAR
**TITLE: Murray-von Neumann dimension and Jones towers of factors.

SPEAKER: Shuler Hopkins, UTK

TIME: 2:30 -3:20pm

ROOM: Ayres 113

ABSTRACT: In this talk, we will introduce the concept of the dimension of a Hilbert space over a von Neumann algebra in order to define the Jones index of an inclusion of finite factors $N\subset M$ (an invariant for the 'position' of N in M). We use this inclusion to perform Jones's "basic construction" to obtain a new factor containing M. Iterating this procedure yields a tower of factors satisfying remarkable properties. In Vaughn Jones's seminal paper "Index for Subfactors" these properties are used to prove the surprising result that not every real number >1 appears as a Jones Index.

**COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
**TITLE: Modeling in Mathematical Biology

SPEAKER: Speaker: Tricia Phillips, UTK

TIME: 3:35 PM

ROOM: Ayres 112

ABSTRACT: I will give an overview of modeling in mathematical biology and discuss specific applications.

**Thursday, Nov. 21**

**DIFFERENTIAL EQUATIONS
**TITLE: On Masuda's uniqueness theorem for the Navier-Stokes Equations.

SPEAKER: Timothy Robertson, UTK

TIME: 2:10- 3pm

ABSTRACT: In 1933 Leray famously proved the existence of weak solutions of the Navier-Stokes equations with $L^{2}$ initial data. However, the uniqueness of these solutions remained an open question. Here we present Masuda's proof of weak-strong uniqueness in the critical case in dimension three, and an ancillary result of Kozono and Sohr.

**ALGEBRA SEMINAR
**TITLE: Cancellation of finite-dimensional Noetherian modules

SPEAKER: Dr. Robin Baidya, UTK

TIME: 3:30 – 4:30pm

ROOM: Ayres 113

ABSTRACT: The Module Cancellation Problem asks when isomorphic direct summands of a module have isomorphic complements. In other words, if K, L, and M are modules over a ring S such that the direct sum of K and L is isomorphic to the direct sum of K and M, the question is when L is isomorphic to M. In a forthcoming paper, we prove that cancellation holds if S is commutative; K and M are Noetherian; K has finite dimension; and, after localizing at any prime ideal p in the support of K, the module M admits a direct-sum decomposition in which the number of times K appears exceeds the dimension of S/p. Our finding yields examples inaccessible by cancellation theorems of Bass, De Stefani-Polstra-Yao, Evans, and Warfield: In the first two cases, K is required to be projective, whereas we do not impose such a condition; in the last two cases, there are constraints on the stable rank of the endomorphism ring of K over S that we have been able to obviate. In this talk, we will present three concrete examples that satisfy the hypotheses in our cancellation theorem but fail to meet the criteria of the other theorems we have mentioned.

**MATHEMATICAL DATA SCIENCE SEMINAR
**TITLE: A Review of Contemporary Topological Analyses of Machine Learning

SPEAKER: Ephy Love, UTK

TIME: 2:10-3:25PM

ROOM: Ayres 111

ABSTRACT: We will review four recent papers on the application of topological data analysis (TDA) to machine learning. There is tremendous interest in developing better explanatory tools for highly complex and non-linear machine learning methods. TDA is a promising toolbox for this line of work, both in post hoc interpretation and in interpretable feature construction. Carlson et al.'s paper "Topological Approaches to Deep Learning" was published less than a year ago and already has 8 citations on Google Scholar. We will examine basic model constructions, analyses of datasets, presentations of results and promising research avenues discussed in four papers published in the last year.

Papers to be Covered:

1. Ayasdi. (2018). Topological Data Analysis Based Approaches to Deep Learning.

2. Brüel-Gabrielsson, R., Nelson, B. J., Dwaraknath, A., Skraba, P., Guibas, L. J., & Carlsson, G. (2019). A Topology Layer for Machine Learning. ArXiv:1905.12200 [Cs, Math, Stat]. Retrieved from http://arxiv.org/abs/1905.12200

3. Carlsson, G., & Gabrielsson, R. B. (2018). Topological Approaches to Deep Learning. ArXiv:1811.01122 [Cs, Math, Stat]. Retrieved from http://arxiv.org/abs/1811.01122

4. Garin, A., & Tauzin, G. (2019). A Topological “Reading” Lesson: Classification of MNIST using TDA. ArXiv:1910.08345 [Cs, Math, Stat]. Retrieved from http://arxiv.org/abs/1910.08345

GEOMETRIC ANALYSIS SEMINAR

TITLE: Isoperimetric problems in Lorentzian manifolds

SPEAKER: Julian Scheuer, Columbia University

TIME: 4:00pm

ROOM: Ayres 113

ABSTRACT: Isoperimetric problems in Lorentzian manifoldsSpeaker: Julian Scheuer ( Columbia University) Time:4:00 – 5:00pmAbstract: The classical isoperimetric and Minkowski inequalities in the Euclidean space relate the enclosed volume, the surface area and the total mean curvature of certain hypersurfaces. In this talk we present a curvature flow approach to prove properly defined analogues in certain classes of Lorentzian manifolds.

*If you are interested in giving or arranging a talk
for one of our seminars or colloquiums, please review our
calendar. *

*If you have questions, or a date you would like to confirm,
please contact Dr. Christopher Strickland, cstric12@utk.edu *

**Past notices:**