Video Lectures

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...

The Gaiotto-Moore-Witten "Algebra of the Infrared" allows one to construct the category of supersymmetric boundary conditions for a wide class of massive N=(2,2) QFTs in two dimensions. In particular, it applies to N=(2,2) QFTs defined by a Morse...

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...

In this talk, we will consider a stabilized version of the fundamental existence problem of symplectic structures (cf. Open Problem 1 in McDuff & Salamon). Given a formal symplectic manifold, i.e. a closed manifold M

with a non-degenerate 2-form and...

While the vast majority of the light from our galaxy comes from the Galactic disk, the vast majority of the mass of the Milky Way (MW) is in its dark matter halo. Because we cannot directly observe the MW's dark matter halo, we must use luminous...