# Special Year 2020-21: Virtual Workshop on Representation Theory and Geometry

### Workshop on Representation Theory and Geometry

April 03, 2021 | 12:00pm - 1:00pm

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)...

### Workshop on Representation Theory and Geometry

April 03, 2021 | 10:30am - 11:30am

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...

### Workshop on Representation Theory and Geometry

April 03, 2021 | 9:00am - 10:00am

In an ongoing project of D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at...

### Workshop on Representation Theory and Geometry

April 02, 2021 | 5:00pm - 6:00pm

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...

### Workshop on Representation Theory and Geometry

April 02, 2021 | 3:30pm - 4:30pm

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...

### Workshop on Representation Theory and Geometry

April 02, 2021 | 2:00pm - 3:00pm

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...

### Workshop on Representation Theory and Geometry

April 01, 2021 | 12:00pm - 1:00pm

Let $G$ be a complex reductive group, $G^*$ its dual Poisson-Lie group, and $g$ the Lie algebra of $G$. $G$-valued Stokes phenomena were exploited by P. Boalch to linearise the Poisson structure on $G^*$. I will explain how $Ug$-valued Stokes...

### Workshop on Representation Theory and Geometry

April 01, 2021 | 10:30am - 11:30am

Using the arithmetics of quantum numbers we construct some “approximations” of tilting modules for reductive algebraic groups that might be useful for understanding the generational patterns of tilting characters conjectured by Lusztig and...

### Workshop on Representation Theory and Geometry

April 01, 2021 | 9:00am - 10:00am

I will explain the construction of an action of the Hecke category on the principal block of representations of a connected reductive algebraic group over an algebraically closed field of positive characteristic, obtained in joint work with Roman...

### Workshop on Representation Theory and Geometry

March 31, 2021 | 5:00pm - 6:00pm

What can one say about the fields of values of irreducible complex characters $\chi$ of a given finite group $G$? In particular when $G$ is a finite (quasi)simple group? What about the McKay situation'', i.e. when the degree of $\chi$ is coprime...