Video Lectures

Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over finite...

We discuss constraints on exact Lagrangian embeddings obtained from considering bordism classes of flow modules over Lagrangian Floer flow categories. This talk reports on joint work with Noah Porcelli.

A graph G is said to be Ramsey for a tuple of graphs (H1,...,Hr) if every r-coloring of the edges of G contains a monochromatic copy of Hi in color i, for some i. A fundamental question at the intersection of Ramsey theory and the theory of random...

The central problem of physics and quantum chemistry is to find the ground state energy of some physical system governed by quantum mechanics.  In mathematical terms, this means finding the lowest eigenvalue of some linear operator on a vector space...

We discuss an application of the SUSY approach to the analysis of spectral characteristics of hermitian and non hermitian random band matrices. In 1D case the obtained integral representations for correlation functions of characteristic polynomials...

The presence of hyperbolic periodic orbits or invariant sets often has an affect on the global behavior of a dynamical system. In this talk we discuss two theorems along the lines of this phenomenon, extending some properties of Hamiltonian...

It is known that a p-adic family of modular forms does not necessarily specialize into a classical modular form at weight one, unlike the modular forms of weight 2 or higher. We will explain how this obstruction to classicality leads to a "derived"...

I will describe the main ideas that go into the proof of the (unramified, global) geometric Langlands conjecture. All of this work is joint with Gaitsgory and some parts are joint with Arinkin, Beraldo, Chen, Faergeman, Lin, and Rozenblyum. I will...

I will discuss a recent proof of new cases of the Hilbert-Smith conjecture for actions by homeomorphisms of symplectic nature. In particular, it rules out faithful actions of the additive p-adic group in this setting and provides further...

In this talk, we will present a new approach for approximating large independent sets when the input graph is a one-sided expander—that is, the uniform random walk matrix of the graph has second eigenvalue bounded away from 1. Specifically, we show...