Video Lectures

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...

Finding regular subgraphs can be useful. Many results assume a graph is regular or are easier to prove when they are. In 1975, Erdős and Sauer asked for an estimate, for any constant r, on the maximum number of edges an n-vertex graph can have...

I will describe and argue the existence of contact non-squeezing phenomena in contact lens spaces and in strongly orderable prequantizations.

The proof is based on the construction of contact capacities coming from spectral selectors defined on the...

We show that for every quadratic extension of number fields K/F, there exists an abelian variety A/F of positive rank whose rank does not grow upon base change to K. By work of Shlapentokh, this implies that Hilbert's tenth problem over the ring of...