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SUMMARY:Tom Gannon (University of Texas)
DTSTART:20220330T200000Z
DTEND:20220330T210000Z
DTSTAMP:20260423T035539Z
UID:MITLie/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/52/">
 Categorical Representation Theory and the Coarse Quotient</a>\nby Tom Gann
 on (University of Texas) as part of MIT Lie groups seminar\n\nLecture held
  in 2-142.\n\nAbstract\nThe main theorem of this talk will be that one can
  understand a "dense open" subset of DG categories with an action of a spl
 it reductive group G over a field of characteristic zero entirely in terms
  of its root datum. We will start by introducing the notion of a categoric
 al representation of G and discuss some motivation. Then\, we will discuss
  some of the main technical tools involved in making the statement of the 
 main theorem precise\, including discussion of the "coarse quotient" of th
 e dual maximal Cartan by the affine Weyl group. We will also discuss how s
 heaves on this coarse quotient can be identified with bi-Whittaker sheaves
  on G\, obtaining symmetric monoidal upgrade of a result of Ginzburg and L
 onergan\, and then give an outline of the proof of the main theorem. Time 
 permitting\, we will discuss some applications of these categorical repres
 entation theoretic ideas which prove a modified version of a conjecture of
  Ben-Zvi and Gunningham on the essential image of parabolic restriction.\n
LOCATION:https://researchseminars.org/talk/MITLie/52/
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