# Next Week's Events

## Seminars

Click on seminar heading to go to seminar page.

• ### Algebra Seminar

Monday October 4, 2021 at 13:30, Wachman 617
For the Grothendieck-Teichmueller group to GT-shadows

Vasily Dolgushev, Temple University The Grothendieck-Teichmueller group GT introduced by V. Drinfeld in 1990 connects topology to number theory in fascinating way. GT receives an injective homomorphism from the absolute Galois group G_Q of rational numbers, it acts on Grothendieck's child's drawings and this action is compatible with that of G_Q. I will start this series of talks with defining what I call the gentle version of GT. In the subsequent talks, we will introduce the groupoid of GT-shadows and explain its link to (the gentle version of) GT.

• ### Analysis Seminar

Monday October 4, 2021 at 14:30, Wachman 617

Jeongsu Kyeong, Temple University

Among other things, integral identities of Rellich type allow one to deduce the $L^{2}(\partial \Omega)$ equivalence of the tangential derivative and the normal derivative of a harmonic function with a square integrable non-tangential maximal function of its gradient in a given Lipschitz domain $\Omega \subset \mathbb{R}^{n}$. In this survey talk, I will establish the integral identities in $\mathbb{R}^{n}$ and I will illustrate the role that the aforementioned equivalence plays in establishing invertibility properties of singular integral operators of layer potential type associated with the Laplacian in Lipschitz domains in $\mathbb{R}^{2}$, through an interplay between PDE, Harmonic Analysis, and Complex Analysis methods.

• ### Geometry and Topology Seminar

Tuesday October 5, 2021 at 14:30, Wachman 617

Abstract TBA

• ### Probability Seminar

Tuesday October 5, 2021 at 15:30, Temple (Wachman Hall 617)
Singularities in the spectrum of random block matrices

David Renfrew, SUNY Binghamton

We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this singularity depends on the relative positions of the zero submatrices. We provide a classification of all possible singularities and determine the exponent in the density blow-up.

## Conferences

There are no conferences next week.