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CATEGORIES:Number Theory Seminar
SUMMARY:Affine Deligne-Lusztig varieties and Generalized a
ffine Springer fibers - Xuhua He\, Chinese Univers
ity of Hong Kong
DTSTART;TZID=Europe/London:20210504T143000
DTEND;TZID=Europe/London:20210504T153000
UID:TALK158695AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/158695
DESCRIPTION:The notion of affine Springer fiber was introduced
by Kazhdan and Lusztig in 1988. It plays a crucia
l role in the geometric representation theory and
the Langlands program. The generalized affine Spri
nger fibers were first studied by Kottwitz and Vie
hmann for the hyperspecial level structure in 2012
and by Lusztig for arbitrary parahoric level stru
cture in 2015. Many geometric properties for the h
yperspecial level structure were further studied b
y Bouthier and Chi.\n\nIn this talk\, I will propo
se a new approach to study the generalized affine
Springer fibers. The key observation is that the a
ffine Deligne-Lusztig varieties\, in some sense\,
may be regarded as the ``shadow'' of generalized a
ffine Springer fibers. I will also explain some in
gredients used to deduce some geometric properties
(nonemptiness\, dimension\, irreducible component
s) of generalized affine Springer fibers from the
properties of the affine Deligne-Lusztig varieties
. This talk is based a work in progress.
LOCATION:Online
CONTACT:Rong Zhou
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