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SUMMARY:Affine Deligne-Lusztig varieties and Generalized affine Springer f
 ibers - Xuhua He\, Chinese University of Hong Kong
DTSTART:20210504T133000Z
DTEND:20210504T143000Z
UID:TALK158695@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:The notion of affine Springer fiber was introduced by Kazhdan 
 and Lusztig in 1988. It plays a crucial role in the geometric representati
 on theory and the Langlands program. The generalized affine Springer fiber
 s were first studied by Kottwitz and Viehmann for the hyperspecial level s
 tructure in 2012 and by Lusztig for arbitrary parahoric level structure in
  2015. Many geometric properties for the hyperspecial level structure were
  further studied by Bouthier and Chi.\n\nIn this talk\, I will propose a n
 ew approach to study the generalized affine Springer fibers. The key obser
 vation is that the affine Deligne-Lusztig varieties\, in some sense\, may 
 be regarded as the ``shadow'' of generalized affine Springer fibers. I wil
 l also explain some ingredients used to deduce some geometric properties (
 nonemptiness\, dimension\, irreducible components) of generalized affine S
 pringer fibers from the properties of the affine Deligne-Lusztig varieties
 . This talk is based a work in progress.
LOCATION:Online
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