Video Lectures

The theta correspondence of Roger Howe gives a way to connect representations of different classical groups. We aim to geometrize the theta correspondence for groups over finite fields in the spirit of Lusztig's character sheaves. Given a reductive...

Indistinguishability obfuscation, introduced by [Barak et. al. Crypto’2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new...

We consider the universality of existence and saturation of asymptotic bounds in various quantities in 2D CFT. In particular, we focus on previously derived upper and lower bounds on the number of operators in a window of scaling dimensions [Δ−δ,Δ+δ...

Mathematics is an extremely deep and extensive subject, but amazingly we are surrounded by easily stated mathematical problems about which almost nothing is known. These kinds of problems tantalize mathematicians with their combination of simplicity...

Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The...

Let \o be an order in a totally real field, say F. Let K be an odd-degree totally real field. Let S be a finite set of places of K. We study S-integral K-points on integral models H_\o of Hilbert modular varieties because not only do said varieties...

I will present the first results of the survey of all white dwarfs (WD) that were observed in the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) using the Visible Integral-field Replicable Unit Spectrograph (VIRUS). The final outcome will be...

This talk will be an exposition of a recent paper of Bezrukavnikov-Gaitsgory-Mirkovic-Riche-Rider giving an Iwahori-Whittaker model for the Satake category. The main point is that their argument works for modular coefficients. I will give some...

A sofic approximation to a countable discrete group is a sequence of finite models for the group that generalizes the concept of a Folner sequence witnessing amenability of a group and the concept of a sequence of quotients witnessing residual...

The modular representation theory of a finite group naturally breaks into different pieces called blocks, and the defect of a block is a sort of measure of its complexity. I will recall some basic aspects of this theory, and then give the complete...