About this Event
Speaker: Andrei Ionov (Boston College)
Where: In-Person at MIT Room 2-135, and on
Zoom: https://mit.zoom.us/j/93574730255
Title: Character sheaves, Koszul duality and link invariants
Abstract:
I will report on a new approach to interpreting the category of character sheaves as a monoidal center of the torus-equivariant version of the Hecke category. The benefits of this approach are that it at the same time stays completely within the realm of triangulated categories, works independently of sheaf-theoretic set up and goes beyond the case of unipotent monodromic sheaves. In particular, it allows to give a new proof, independent of sheaf-theoretic setting, of the fact that the Drinfeld center of the abelian Hecke category is equivalent to the abelian category of unipotent character sheaves. I will further use the construction to establish a mixed Koszul self-duality for the derived category of character sheaves. This in turn has an application to symmetry in Khovanov-Rozansky homology theories and the generalizations of these theories to links due to Gorsky-Hogancamp.
The talk is based on several projects, both published and in preparation, joint in various combinations with R. Bezrukavnikov, R. Gonin, Q.P. Ho, P. Li, K. Tolmachov and Y. Varshavsky.
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