Abstract: I will discuss applications of geometric representation theory to topological and quantum invariants of character stacks. In particular, I will explain how generalized Springer correspondence for class D-modules and Koszul duality for Hecke categories encode surprising structure underlying the homology of character stacks of surfaces (joint work with David Ben-Zvi and David Nadler). I will then report on some work in progress with David Jordan and Pavel Safronov concerning a q-analogue of these ideas. The applications include an approach towards Witten’s conjecture on the fi dimensionality of skein modules, and methods for computing these dimensions in certain cases.
Recording during the meeting "Symplectic Representation Theory" the April 2, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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Sam Gunningham: Character stacks and (q−)geometric representation theory amulet meaning | |
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