### Seminars and Colloquiums 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:

Nov. 11, 2019

Nov. 4, 2019

Oct. 28, 2019

Oct. 21, 2019

Oct. 14, 2019

Oct. 7, 2019

Sept. 30, 2019

Sept. 23, 2019

Sept. 16, 2019

Sept. 9, 2019

Sept. 2, 2019

Aug. 26, 2019

2018-19

2017-18

###### last updated: November 2019

Department of Mathematics
College of Arts & Sciences

227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320
Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu