Previous Conferences & Workshops

I will motivate the study of the Schubert variety of a pair of linear spaces via Kempf collapsing of vector bundles. I'll describe equations defining this variety and how this yields a simplicial complex determined by a pair of matroids which...

Let w be a word in a free group. A few years ago, Magee and I, relying on a work of Calegari, discovered that the stable commutator length of w, which is a well-studied topological invariant, can also be defined in terms of certain Fourier...

I will describe the duality of incompressible Navier-Stokes fluid dynamics in three dimensions, leading to its reformulation in terms of a one-dimensional momentum loop equation.
The decaying turbulence is a solution of this equation equivalent to a...

In this talk, I will elaborate on the main technical component of our PCP—the construction of routing protocols on high-dimensional expanders (HDX) that can withstand a constant fraction of edge corruptions. We consider the following routing problem...

Studying the \’etale cohomology of Shimura varieties with Hecke and Galois actions provides an avenue toward understanding the Langlands correspondence. 
While the structure of the rational cohomology groups is predicted conjectures of Kottwitz and...

A promenade in Serre's paper, plus some related results of mine.

The theory of probabilistically checkable proofs (PCPs) shows how to encode a proof for any theorem into a format where the theorem's correctness can be verified by making only a constant number of queries to the proof. The PCP Theorem [ALMSS] is a...

Recent progress on character bounds for groups of Lie type makes it feasible in many cases to find the asymptotic growth, for fixed q and n tending to infinity, of the number of n-dimensional representations of a Fuchsian group G over the field with...