Geometric Representation Theory Seminar

On the Gaiotto conjecture I: statement

Time: Wed., 10:30-11:30 am, July 5, 2023

Abstract

A conjecture of Davide Gaiotto predicts a geometrization of the category of representations of the quantum supergroup. This geometrization is given by the category of twisted D-modules on the affine Grassmannian with a certain equivariant condition. In this talk, we will introduce the precise statement of the Gaiotto conjecture and the recent progress. This is based on the joint works with R. Travkin, and also the works of A. Braverman, M. Finkelberg, V. Ginzburg and R.Travkin.

On the Gaiotto conjecture II: sketch of proof

Time: Fri.,10:30-11:30am, July 7, 2023

Abstract

In this talk, our goal is to introduce the tools used in the proof and sketch the proof of the Gaiotto conjecture for GL(M|N).

Speaker

I am interested in Quantum Geometric Langlands Program. I’m currently working on Gaiotto conjecture with my postdoc advisor Professor Mikhail Finkelberg, Professor Alexander Braverman, and Roman Travkin. To be more precise, we hope to relate the category of representations of the quantum supergroups to the category of twisted D-modules on affine flags and affine Grassmannians.