Click on seminar heading to go to seminar page.
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.
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.
Radhika Gupta, Temple University
Abstract TBA
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.
There are no conferences next week.