Video Lectures

In a vertex expanding graph, every small subset of vertices neighbors many different vertices. Random graphs are near-optimal vertex expanders; however, it has proven difficult to create families of deterministic near-optimal vertex expanders, as the...

A symplectic embedding of a disjoint union of domains into a symplectic manifold M is said to be of Kahler type (respectively tame) if it is holomorphic with respect to some (not a priori fixed) integrable complex structure on M which is compatible...

The quantum unique ergodicity conjecture of Rudnick and Sarnak concerns the mass equidistribution in the large eigenvalue limit of Laplacian eigenfunctions on negatively curved manifolds. This conjecture has been resolved by Lindenstrauss when this...

We discuss a one-phase degenerate free boundary problem which arises from the minimization of the so-called Alt-Phillips functional. We establish partial regularity results for the free boundary and discuss the rigidity of global minimizers when...

I will discuss pointwise ergodic theory as it developed out of Bourgain's work in the 80s, leading up to my work with Mirek and Tao on bilinear ergodic averages.

Let C be a class of metric spaces. We consider the following computational metric embedding problem: given a vector x in R^{n choose 2} representing pairwise distances between n points, change the minimum number of entries of x to ensure that the new...

A finite set system is union-closed if for every pair of sets in the system their union is also in the system.  Frankl in 1979 conjectured that for any such system there exists an element which is contained in ½ of the sets in that system (the only...

Given a convex billiard table, one defines the set  swept by locally maximizing orbits for convex billiard. This is a remarkable closed invariant set which does not depend (under certain assumptions) on the choice of the generating function. I shall...

Discrepancy theory provides a powerful approach to improve upon the bounds obtained by a basic application of the probabilistic method. In recent years, several algorithmic approaches have been developed for various classical results in the area. In...

P-adic non abelian Hodge theory, also known as the p-adic Simpson correspondence, aims at describing p-adic local systems on a smooth rigid analytic variety in terms of Higgs bundles. I will explain in this talk why the « Hodge-Tate stacks » recently...