Video Lectures

Combinatorial Invariance: a Case Study of Pure Math / Machine  Learning Interaction

The combinatorial invariance conjecture is a fascinating conjecture in Representation Theory. Basically it says that certain important polynomials ("Kazhdan-Lusztig...

The signature of a knot K in the 3-sphere is a classical  invariant that gives a lower bound on the genera of compact oriented surfaces in the 4-ball with boundary K. We say that K is hyperbolic if its complement admits a complete, finite volume...

Proving a 2009 conjecture of Itai Benjamini, we show:  For any C, there is a greater than 0 such that for any simple random walk on an n-vertex graph G, the probability that the first Cn steps of the walk hit every vertex of G is at most exp[-an]. ...

I will talk about an ongoing project that explores the construction of high dimensional Legendrian spheres from supporting open books and contact structures. The input is a Lagrangian disk filling of a Legendrian knot in the binding. We try to...

I will explain the construction of a new class of Liouville domains that live in a complex torus of arbitrary dimension, whose boundary dynamics encodes information about the singularities of a toric compactification. The primary motivation for this...

In this talk, we will study the Floer Homology barcodes from a dynamical point of view. Our motivation comes from recent results in symplectic topology using barcodes to obtain dynamical results. We will give the ideas of new constructions of...

Let N and p greater than or equal to 5 be primes such that p divides N−1. In his landmark paper on the Eisenstein ideal, Mazur proved the p-part of the BSD conjecture for the p-Eisenstein quotient J(p) of J0(N) over Q. Using recent results and...

The Nielsen-Thurston theory of surface homeomorphism can be thought of as a surface analogue to the Jordan Canonical Form.  I will discuss my progress in developing a similar decomposition for free group automorphisms. (Un)Fortunately, free group...

We will discuss the regularity properties and size of generic level sets of functions that satisfy weak local Lipschitz conditions.

Two recent and seemingly-unrelated techniques for proving mixing bounds for Markov chains are:

(i) the framework of Spectral Independence, introduced by Anari, Liu and Oveis Gharan, and its numerous extensions, which have given rise to several...