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SUMMARY:Logarithmic differential forms on Bott-Samelson varieties and brai
 d relations
DTSTART:20220505T131500
DTEND:20220505T150000
DTSTAMP:20260407T025829Z
UID:5537951b34c4e666714ac4445eeac5ec180d78e9c3a944541dc7b123
CATEGORIES:Conferences - Seminars
DESCRIPTION:Sergey Arkhipov (Aarhus University)\nBraid relations in the co
 herent version of the affine Hecke category were established via a delicat
 e study of Steinberg variety\, by Bezrukavnikov and Riche. The talk is dev
 oted to an alternative approach to establishing braid relations in a versi
 on of affine Hecke category developed in the thesis of my student Sebastia
 n Orsted.\n\nWe begin with proposing a realization of affine Hecke categor
 y Koszul dual to the one of Bezrukavnikov-Riche: we define a category of e
 quivariant modules over the ring of differential forms on a reductive alge
 braic group G\, equipped with convolution monoidal structure. Then we intr
 oduce the candidates for the braid group generators given by DG-modules of
  logarithmic differential forms on the minimal parabolic subgroups. The pr
 oof of braid relations goes via the study of logarithmic differential form
 s on large Bott-Samelson varieties and is based on the following observati
 on.\n\nLet X be a desingularization of the variety Y such that the preimag
 e of a divisor containing singularities of Y in X is a divisor with normal
  crossings. Then the direct image of the sheaf of logarithmic differential
  forms on X to Y depends on Y\, not on the resolution of singularities X.\
 n\nWe outline the calculation leading to the proof of this statement.
LOCATION:CM 0 9 https://plan.epfl.ch/?room==CM%200%209
STATUS:CONFIRMED
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