# 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...

### Representation Theory & Combinatorics of the Symmetry Group and Related Structures III

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 first part of this talk, I'll explain a geometric categorification of the Hecke algebra in terms of perverse sheaves on the flag variety. In the second part, we'll study the affine Hecke algebra. In this case, there are two categorical...

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...

### Representation Theory & Combinatorics of the Symmetry Group and Related Structures II

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...