Video Lectures

We will explore certain $C^0$-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is related to the Rokhlin property of the group of...

I will discuss recent results for algebraicity of critical values of Spin L-functions for GSp_6. I will also discuss ongoing work toward the construction of p-adic L-functions interpolating these values. I will explain how this work fits into the...

More languages and literary traditions existed simultaneously in the medieval Middle East than any individual scholar can hope to master.  Disciplinary norms have mandated that scholars focus on one or perhaps two languages, but the actual...

In 1999, Pitman and Stanley introduced the polytope bearing their name along with a study of its faces, lattice points, and volume. This polytope is well-studied due to its connections to parking functions, lattice path matroids, generalized...

The plan of the talk is to describe joint work with A. Brown and Z. Wang on the smooth classification of actions of lattices in SL(n,ℝ)

on n−1 dimensional manifolds. The method is also amenable to show rigidity for some boundary actions.

A minimal partition is a decomposition of a manifold into disjoint sets that minimizes a spectral energy functional. In the bipartite case minimal partitions are closely related to eigenfunctions of the Laplacian, but in the non-bipartite case they...

In a series of papers with Alexander Ritter, we construct a symplectic cohomology for open non-convex symplectic manifolds that admit pseudo-holomorphic C*-actions. Out of this construction, we get a filtration on ordinary cohomology of these...

Cayley graphs provide interesting bridges between graph theory, additive combinatorics and group theory. Fixing an ambient finite group, random Cayley graphs are constructed by choosing a generating set at random. These graphs reflect interesting...

I will talk about a proof of local-global compatibility at p for higher coherent cohomology mod p in weight one for Hilbert modular varieties at an unramified prime, assuming we are not in middle degree. I will discuss some key ingredients to the...

In their 1971 study of telephone switching circuitry, Graham and Pollak designed a novel addressing scheme that was better suited for the faster communication required by computers. They introduced the distance matrix of a graph, and used its...