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Seminar

GRTA seminar: Modular Koszul duality for the Hecke category February 13, 2018 (02:00 PM PST - 03:00 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Shotaro Makisumi (Columbia University)
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The Hecke category is a categorification of the Hecke algebra that plays an important role in geometric representation theory. I will discuss a monoidal Koszul duality for the Hecke category in positive characteristic (in cases arising from geometry), categorifying a certain involution of the Hecke algebra. This result has consequences for the modular representation theory of reductive groups. To keep prerequisites to a minimum, I will focus on the case of SL_2 and explain the key constructions using a combinatorial/algebraic incarnation of the Hecke category (Soergel bimodules). In particular, the phrases "parity/perverse sheaves" will only be mentioned in passing. (Joint with P.N. Achar, S. Riche, and G. Williamson.)

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