# Video Lectures

Differential delay equations arise very naturally, but they are much more complicated than ordinary differential equations. Polyfold theory, originally developed for the study of moduli spaces of pseudoholomorphic curves, can help to understand...

A central problem in low-dimensional topology asks which homology 3-spheres bound contractible 4-manifolds and homology 4-balls. In this talk, we address this problem for plumbed 3-manifolds and we present the classical and new results together...

This is intended to complement the recent talk of Pham Huu Tiep in this seminar but will not assume familiarity with that talk. The estimates in the title are upper bounds of the form |?(g)|??(1)?, where ? is irreducible and ? depends on the size 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...

### 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...