Speaker: Pramod Achar
Title: The Arkhipov-Bezrukavnikov-Ginzburg equivalence
Date: February 5, 2025
Abstract: The famous paper "ABG" is about the relationship between the following four (derived) categories:
(1) Representations of a quantum group at a root of unity
(2) Representations of a quantum Borel that are trivial for the "small" quantum Borel
(3) Coherent sheaves on the Springer resolution
(4) Perverse sheaves on the affine Grassmannian
I'll explain some foundational things about all four categories, including some Ext-calculations that hint at the relationship between them. I'll also discuss how to construct functors between them. The main results of ABG state (roughly) that all four are equivalent, and I will outline the argument for these results.