Video Lectures

I will first give an overview of ECH. Then I will describe how to compute ECH in the Morse-Bott setting a la Bourgeois. I will discuss some classes of examples where this approach works. Finally I will sketch the gluing results that allow us to...

The theory of "random surfaces" has emerged in recent decades as a significant field of mathematics, lying somehow at the interface between geometry, probability, and mathematical physics. I will give a friendly (I hope) colloquium-level overview of...

Sampling from high-dimensional, multimodal distributions is a computationally challenging and fundamental task.  This talk will focus on a family of random instances of such problems described by random quadratic potentials on the hypercube known as...

Weinstein domains and their symplectic invariants have been extensively studied over the last 30 years. Little is known about non-Weinstein Liouville domains, whose first instance is due to McDuff. I will describe two key examples of such domains in...

I will motivate the study of coproducts and describe a new coproduct structure on the symplectic cohomology of Liouville manifolds. Time permitting, I will indicate how to compute it in an example to show that it's not trivial. This is based on my...

I will discuss how the Deligne-Mumford compactification of curves arises from the uncompactified moduli spaces of curves as a result of some algebraic operations related to (pr)operadic structures on the moduli spaces. I will describe how a...

If a set of integers is syndetic (finitely many translates cover the integers), must it contain two integers whose ratio is a square?  No one knows.  In the broader context of the disjointness between additive and multiplicative configurations and...

A powerful technique developed and extended in the past decade in communication complexity is the so-called "lifting theorems."  The idea is to translate the hardness results from "easier" models, e.g., query complexity, polynomial degrees, to the...

In this talk, we show a strong XOR lemma for bounded-round two-player randomized communication.  For a function f:X×Y→{0,1}, the n-fold XOR function f^⊕n:X^n×Y^n→{0,1} maps n input pairs (x_1,...,x_n), (y_1,...,y_n) to the XOR of the n output bits f...

We discuss new results on lozenge tilings on an infinite cylinder, which may be analyzed using the periodic Schur process introduced by Borodin. Under one variant of the q^vol measure, corresponding to random cylindric partitions, the height...