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SUMMARY:Xuhua He (Chinese University of Hong Kong)
DTSTART:20210504T133000Z
DTEND:20210504T143000Z
DTSTAMP:20260421T151706Z
UID:CamNT/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CamNT/12/">A
 ffine Deligne-Lusztig varieties and Generalized affine Springer fibers</a>
 \nby Xuhua He (Chinese University of Hong Kong) as part of Cambridge Numbe
 r Theory Seminar\n\n\nAbstract\nThe notion of affine Springer fiber was in
 troduced by Kazhdan and Lusztig in 1988. It plays a crucial role in the ge
 ometric representation theory and the Langlands program. The generalized a
 ffine Springer fibers were first studied by Kottwitz and Viehmann for the 
 hyperspecial level structure in 2012 and by Lusztig for arbitrary parahori
 c 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 new approach to study the generalized affine Springer f
 ibers. The key observation is that the affine Deligne-Lusztig varieties\, 
 in some sense\, may be regarded as the ``shadow'' of generalized affine Sp
 ringer fibers. I will also explain some ingredients used to deduce some ge
 ometric properties (nonemptiness\, dimension\, irreducible components) of 
 generalized affine Springer fibers from the properties of the affine Delig
 ne-Lusztig varieties. This talk is based a work in progress.\n
LOCATION:https://researchseminars.org/talk/CamNT/12/
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