11/27 at 17:30 in 507

Cailan Li 

Title: Soergel Bimodules, Character Sheaves, and Gomi's Trace

Abstract: 

In the early 1990's, Soergel found a different proof of the illustrious Kazhdan-Lusztig conjectures using "mostly" algebraic techniques, via Soergel (bi)modules. Since their discovery, Soergel bimodules have been a cornerstone of representation theory and link homology and in recent years has attracted a lot of attention due to their diagrammatic incarnations by Elias-Khovanov and Elias-Williamson. In the first part of this talk, we will explain the motivation and background behind Soergel bimodules and talk about recent work giving diagrammatics for  Ext groups between Soergel Bimodules in rank 2. In the second part of the talk, we will explain how Ext groups of Soergel Bimodules are connected to (unipotent) character sheaves and show how in rank 2 they categorify Gomi's Trace, a generalization of Markov's trace to any finite Coxeter group.