Video Lectures

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...

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...

I will introduce a new structure on (relative) Symplectic Cohomology defined in terms of a PROP called the “Plumber’s PROP.” This PROP consists of nodal Riemann surfaces, of all genera and with multiple inputs and outputs, satisfying a condition...

The possibility that some of the black holes in the universe have a non-stellar origin and that they play a significant role in cosmology - including being some or all of the dark matter - is both timely and intriguing. I will review the status of...

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...

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...

I will discuss dilaton gravity with a sine potential, where periodic shifts of the dilaton (that leave the potential invariant) are treated as a redundancy. Most things I will say hold true for generic periodic potentials, but the sine potential is...

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...

We show that two generic, open, convex or concave toric domains in R4 are symplectomorphic if and only if they agree up to reflection. The proof uses barcodes in positive S1-equivariant symplectic homology, or equivalently in cylindrical contact...