Video Lectures

In modern representation theory we often study the category of modules over an algebra, in particular its intrinsic and combinatorial structures. Vice versa one can ask the question: which categories have a given combinatorics? This is the basic...

With an eye toward coordinating with the advanced course, we will start with the representation theory of the symmetric group and related combinatorics. We will focus on the functors of induction and restriction. We will then consider related...

In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of...

In modern representation theory we often study the category of modules over an algebra, in particular its intrinsic and combinatorial structures. Vice versa one can ask the question: which categories have a given combinatorics? This is the basic...

With an eye toward coordinating with the advanced course, we will start with the representation theory of the symmetric group and related combinatorics. We will focus on the functors of induction and restriction. We will then consider related...

A vast array of physical phenomena, ranging from the propagation of waves to the location of quantum particles, is dictated by the behavior of Laplace eigenfunctions. Because of this, it is crucial to understand how various measures of eigenfunction...

The h-principle for the simplification of caustics (i.e. Lagrangian tangencies) reduces a geometric problem to a homotopical problem. In this talk I will explain the solution to this homotopical problem in the case of spheres. More precisely, I will...

I will discuss recent work with Harald Helfgott in which we establish roughly speaking that the graph connecting nn to n±pn±p with pp a prime dividing nn is almost "locally Ramanujan". As a result we obtain improvements of results of Tao and Tao...

The talk introduces the Kazhdan-Lusztig equivalence between the Kazhdan-Lusztig category of representations of affine algebra and category of modules over the quantum group.

I will report on a joint work in progress with K. Coulembier and V. Ostrik. We show that a symmetric tensor category in characteristic p>0 admits a fiber functor to the Verlinde category (semisimplification of Rep(Z/p)) if and only if it has...