Algebraic Geometry Seminar Spring 2017
The seminar meets on Fridays at 2:25 pm in Van Vleck B113.
Here is the schedule for the previous semester.
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Spring 2017 Schedule
|January 20||Sam Raskin (MIT)||W-algebras and Whittaker categories||Dima|
|January 27||Nick Salter (U Chicago)||TBA||Jordan|
|April 7||Vladimir Dokchitser (Warwick)||TBA||Jordan|
W-algebras and Whittaker categories
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.