# Events for 04/16/2021 from all calendars

## Teaching Online Departmental Open Forum

Time: 12:00PM - 1:00PM

Location: Zoom

Speaker: Vanessa Coffelt & Justin Cantu, Texas A&M University

Description: All forums will be from 12:00 pm to 1:00 pm. The topic will be emailed to faculty the week prior to the forum. We will use the following Meeting ID: 979 6560 9771, and will send out the password in the emails.

## Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: Zoom 951 5490 42

Speaker: Yang Liu, SISSA

Title: Hypergeometric Functions and Heat Coefficients on Noncommutative Tori

Abstract: As the counterpart of conformal geometry, modular geometry on noncommutative manifolds explores the basic notions such as metric and curvature in Riemannian geometry (e.g. noncommutative tori) in a purely spectral framework. It was initiated by Connes-Tretkoff’s Gauss-Bonnet theorem on noncommutative two tori. Another milestone is the construction of modular Gaussian curvature due to Connes-Moscovici, which is derived from variation of the second heat coefficient of some Laplacian type operator. In this talk, I would like to report a few observations on the general structures of those heat coefficients. The word “modular” refers to the new ingredient of the coefficients, arising from the interaction between modular automorphisms associated to the volume state and the underlying smooth structure of the noncommutative manifolds. More precisely, one has to upgrade coefficients of local differential expressions from scalars to so-called rearrangement operators that fix various issues caused by the noncommutativity between metric coordinates and their derivatives. Like the notion of genus to a characteristic class, the spectral functions behind the rearrangement operators turn out to be intriguing. That is where hypergeometric functions come into play. The main result is the explicit formula of the second heat coefficient of a more general Laplacian type operator (beyond conformal perturbations studied in the literature). The talk is based on my recent preprint arxiv:2004.05714.

## Mathematical Physics and Harmonic Analysis Seminar

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Cosmas Kravaris, Texas A&M University

Title: On the density of eigenvalues on discrete periodic graphs

Abstract: Using the Floquet-Bloch transform, we show that Zd-periodic graphs have finitely many finite support eigenfunctions up to translations and linear combinations and show that this can be used to calculate the density of eigenvalues. We study the Kagome lattice to illustrate these techniques and generalize the claims to amenable quasi-homogeneous graphs whose acting group has Noetherian group algebra (this includes all virtually polycyclic groups). Finally, we provide a formula for the von Neumann dimension (i.e. density) of eigenvalues on Zd-periodic graphs using syzygy modules.

## Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Songling Shan, Illinois State University

Title: Chromatic index of dense quasirandom graphs

Abstract: Let $G$ be a simple graph with maximum degree $\Delta(G)$. A subgraph $H$ of $G$ is overfull if $|E(H)|>\Delta(G)\lfloor |V(H)|/2 \rfloor$. Chetwynd and Hilton in 1985 conjectured that a graph $G$ on $n$ vertices with $\Delta(G)>n/3$ has chromatic index $\Delta(G)$ if and only if $G$ contains no overfull subgraph. Glock, K\"{u}hn, and Osthus in 2016 showed that the conjecture is true for dense quasirandom graphs with even order, and they conjectured that the same should hold for such graphs with odd order. We show that the conjecture of Glock, K\"{u}hn, and Osthus is affirmative.

## Full Committee L & I Meeting

Time: 3:00PM - 5:00PM

Location: Zoom

, Texas A&M University