Video Lectures

In the Pandora's Box problem, the algorithm is provided with a number of boxes with unknown (stochastic) rewards contained inside them. The algorithm can open any box at some cost, discover the reward inside, and based on these observations can...

Let g be a semisimple Lie algebra. The affine W-algebra associated to g is a topological algebra which quantizes the algebraic loop space of the Kostant slice. It is constructed as a quantum Hamiltonian (alias quantum Drinfeld--Sokolov) reduction of...

The study of totally positive matrices, i.e., matrices with positive minors, dates back to 1930s. The theory was generalised by Lusztig to arbitrary split reductive groups using canonical bases, and has significant impacts on the theory of cluster...

Links of strata in singular spaces are fundamental invariants which govern the topology of small neighbourhoods around points in those strata. This talk will focus on inferring links of strata from incomplete information in three completely...

Given a maximal torus T of a connected reductive group G over a local field F, there does not exist a canonical embedding of the L-group of T into the L-group of G. Generalizing work of Adams and Vogan in the case F=R, we will construct a natural...

In joint work with Andy Manion, we required a generalization of the tensor product of 2-representations in order to reconstruct the 2-dimensional part of Lipshitz-Oszvath-Szabo’s bordered Heegaard-Floer theory. I will discuss this and possible...

The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the local Langlands program is...

In all known explicit computations on Weinstein manifolds, the self-wrapped Floer homology of non-compact exact Lagrangian is always either infinite-dimensional or zero. We will explain why a global variant of this observed phenomenon holds in broad...

Continuation of the talk from last time.

I will explain some recent work on special cases of the Bloch-Kato conjecture for the symmetric cube of certain modular Galois representations. Under certain standard conjectures, this work constructs nontrivial elements in the Selmer groups of...