Video Lectures

The absorption method is a very simple yet surprisingly powerful idea coming from extremal combinatorics which allows one to convert asymptotic results into exact ones. It has produced a remarkable number of success stories in recent years with...

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...

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...