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

date	speaker	title	host(s)
January 20	Sam Raskin (MIT)	W-algebras and Whittaker categories	Dima
January 27	Nick Salter (U Chicago)	Mapping class groups and the monodromy of some families of algebraic curves	Jordan
April 7	Vladimir Dokchitser (Warwick)	TBA	Jordan

Abstracts

Sam Raskin

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.