Video Lectures

I will explain a new construction of an Euler system for the symmetric square of an eigenform and its connection with L-values. The construction makes use of some simple Eisenstein cohomology classes for Sp(4) or, equivalently, SO(3,2). This is an...

Given a linear equation whose principal term is given by a degenerate dispersive pseudo-differential operator, we provide a framework for the construction of degenerating wave packet solutions. As an application, we prove strong ill-posedness for...

The notion of strong stationarity was introduced by Furstenberg and Katznelson in the early 90's in order to facilitate the proof of the density Hales-Jewett theorem. It has recently surfaced that this strong statistical property is shared by...

Incidence bound for points and spheres in higher dimensions generally becomes trivial in higher dimensions due to the existence of the Lenz example consisting of two orthogonal circles in ℝ4, and the corresponding construction in higher dimensions...

Suppose we are given matchings M1,....,MN of size t in some r-uniform hypergraph, and let us think of each matching having a different color. How large does N need to be (in terms of t and r) such that we can always find a rainbow matching of size t...

Let X be a smooth projective variety over the complex numbers. Let M be the moduli space of irreducible representations of the topological fundamental group of X of a fixed rank r. Then M is a finite type scheme over the spectrum of the integers Z...

Contact topology is the study of certain geometric structures on odd dimensional smooth manifolds. A contact structure is a hyperplane field specified by a one form which satisfies a nondegeneracy condition called maximal non-integrability. The...

Efficient verification of computation is fundamental to computer science and is at the heart of the P vs. NP question. Recently it has had growing practical significance, especially with the increasing popularity of blockchain technologies and cloud...

In this talk, I will describe the construction of contact structures on higher-dimensional spheres with exotic fillability properties. These can then me implemented on more general manifolds via connected sum, yielding a host of exotic higher...

I will discuss exact solvability results (in a sense) for scaling limits of interface crossings in critical random-cluster models in the plane with various general boundary conditions.

The results are rigorous for the FK-Ising model, Bernoulli...