BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Minh-Tam Trinh (MIT Mathematics)
DTSTART:20210303T213000Z
DTEND:20210303T223000Z
DTSTAMP:20260423T052448Z
UID:MITLie/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/22/">
 From the Hecke Category to the Unipotent Locus</a>\nby Minh-Tam Trinh (MIT
  Mathematics) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\
 n\nAbstract\nWhen W is the Weyl group of a reductive group G\, we can cate
 gorify its Hecke algebra by means of equivariant sheaves on the double fla
 g variety of G. We will define a functor from the resulting category to a 
 certain category of modules over a polynomial extension of C[W]. We will p
 rove that\, on objects called Rouquier complexes\, our functor yields the 
 equivariant Borel-Moore homology of a generalized Steinberg variety attach
 ed to a positive element in the braid group of W. Some reasons this may be
  interesting: (1) In type A\, the triply-graded Khovanov-Rozansky homology
  of the link closure of the braid is a summand of the weight-graded equiva
 riant homology of this variety. This extends previously-known results for 
 the top and bottom "a-degrees" of KR homology. (2) The "Serre duality" of 
 KR homology under insertion of full twists leads us to conjecture a myster
 ious homeomorphism between pieces of different Steinbergs. (3) We find evi
 dence for a rational-DAHA action on the (modified) homology of the Steinbe
 rgs of periodic braids. It seems related to conjectures of Broué-Michel a
 nd Oblomkov-Yun in rather different settings.\n
LOCATION:https://researchseminars.org/talk/MITLie/22/
END:VEVENT
END:VCALENDAR