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BEGIN:VEVENT
SUMMARY:Yihang Zhu (University of Maryland)
DTSTART:20211004T180000Z
DTEND:20211004T190000Z
DTSTAMP:20260422T212933Z
UID:UMDANTFALL2021/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMDANTFALL20
 21/1/">Stable trace formula for Shimura varieties of abelian type\, I</a>\
 nby Yihang Zhu (University of Maryland) as part of University of Maryland 
 Algebra-Number Theory Seminar Fall 2021\n\nLecture held in Hybrid\, Kirwan
  Hall 3206.\n\nAbstract\nIn this series of three talks\, we report on the 
 joint work with M. Kisin and S. W. Shin. (preprint\, http://math.umd.edu/~
 yhzhu/KSZ.pdf) (The third talk will be given by Shin.)\n\nWe consider the 
 alternating trace of a Hecke operator away from p and a Frobenius power at
  p acting on the compact support cohomology of a Shimura variety of abelia
 n type with hyperspecial level at p. We show that this is equal to the sum
  of the elliptic parts of the stable trace formulas for the endoscopic gro
 ups with respect to well-chosen test functions\, proving a conjecture of K
 ottwitz.\n\nIn the first talk\, we give some historical background\, state
  the problem\, and discuss our strategy of reducing the result to a form o
 f the Langlands-Rapoport Conjecture where certain "controlled twists" are 
 allowed. This form of Langlands-Rapoport strengthens what was proved in ea
 rlier work of Kisin.\n
LOCATION:https://researchseminars.org/talk/UMDANTFALL2021/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihang Zhu (University of Maryland)
DTSTART:20211006T180000Z
DTEND:20211006T190000Z
DTSTAMP:20260422T212933Z
UID:UMDANTFALL2021/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMDANTFALL20
 21/2/">Stable trace formula for Shimura varieties of abelian type\, II</a>
 \nby Yihang Zhu (University of Maryland) as part of University of Maryland
  Algebra-Number Theory Seminar Fall 2021\n\nLecture held in Hybrid\, Kirwa
 n Hall 3206.\n\nAbstract\nIn this series of three talks\, we report on the
  joint work with M. Kisin and S. W. Shin. (preprint\,  http://math.umd.edu
 /~yhzhu/KSZ.pdf) (The third talk will be given by Shin.)\n\nWe consider th
 e alternating trace of a Hecke operator away from p and a Frobenius power 
 at p acting on the compact support cohomology of a Shimura variety of abel
 ian type with hyperspecial level at p. We show that this is equal to the s
 um of the elliptic parts of the stable trace formulas for the endoscopic g
 roups with respect to well-chosen test functions\, proving a conjecture of
  Kottwitz.  \n\nIn the second talk\, we discuss some ingredients in the pr
 oof of the Langlands-Rapoport-tau Conjecture introduced in the first talk.
  In the case of Hodge type\, we use Breuil-Kisin modules and a recent puri
 ty result of Ansch\\"utz to construct certain "non-standard" lattices in t
 he rational Dieudonn\\'e modules of the reductions of special points. Thes
 e lattices serve as "marking points" that play a key role in the proof.\n
LOCATION:https://researchseminars.org/talk/UMDANTFALL2021/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ananth Shankar (University of Wisconsin\, Madison)
DTSTART:20211026T180000Z
DTEND:20211026T190000Z
DTSTAMP:20260422T212933Z
UID:UMDANTFALL2021/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMDANTFALL20
 21/3/">Canonical heights on Shimura varieties and the Andre-Oort conjectur
 e</a>\nby Ananth Shankar (University of Wisconsin\, Madison) as part of Un
 iversity of Maryland Algebra-Number Theory Seminar Fall 2021\n\n\nAbstract
 \nLet S be a Shimura variety. The Andre-Oort conjecture posits that the Za
 riski closure of special points must be a sub Shimura subvariety of S. The
  Andre-Oort conjecture for A_g (the moduli space of principally polarized 
 Abelian varieties) — and therefore its sub Shimura varieties — was pro
 ved by Jacob Tsimerman. However\, this conjecture was unknown for Shimura 
 varieties without a moduli interpretation. I will describe joint work with
  Jonathan Pila and Jacob Tsimerman (with an appendix by Esnault-Groechenig
 ) where we prove the Andre Oort conjecture in full generality.\n
LOCATION:https://researchseminars.org/talk/UMDANTFALL2021/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (Max-Planck Institut Bonn)
DTSTART:20211108T190000Z
DTEND:20211108T200000Z
DTSTAMP:20260422T212933Z
UID:UMDANTFALL2021/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMDANTFALL20
 21/4/">On the Kottwitz conjecture for local shtuka spaces</a>\nby David Ha
 nsen (Max-Planck Institut Bonn) as part of University of Maryland Algebra-
 Number Theory Seminar Fall 2021\n\n\nAbstract\nThe cohomology of local Shi
 mura varieties\, and of more general spaces of local shtukas\, is of funda
 mental interest in the Langlands program. On the one hand\, it is supposed
  to realize instances of the local Langlands correspondence. On the other 
 hand\, there is a tight relationship with the cohomology of global Shimura
  varieties. In recent joint work with Kaletha and Weinstein\, we proved th
 e first general results towards the Kottwitz conjecture\, which predicts h
 ow supercuspidal L-packets contribute to the cohomology of local shtuka sp
 aces. I will review this story\, and give some overview of the ideas which
  enter into our proof. The key idea in our argument - namely\, that the Ko
 ttwitz conjecture should follow from some form of the Lefschetz-Verdier fi
 xed point formula - was already formulated by Michael Harris in the '90s. 
 However\, executing this idea brings substantial technical challenges. I w
 ill try to emphasize the new ingredients which allow us to implement this 
 idea in full generality.\n
LOCATION:https://researchseminars.org/talk/UMDANTFALL2021/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (Max-Planck Institut Bonn)
DTSTART:20211110T190000Z
DTEND:20211110T200000Z
DTSTAMP:20260422T212933Z
UID:UMDANTFALL2021/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMDANTFALL20
 21/5/">Recent developments in etale cohomology</a>\nby David Hansen (Max-P
 lanck Institut Bonn) as part of University of Maryland Algebra-Number Theo
 ry Seminar Fall 2021\n\n\nAbstract\nI'll talk about some recent foundation
 al developments in etale cohomology:\n\n\ni) A flexible six-functor formal
 ism for "Zariski-constructible" sheaves on rigid spaces (joint work with B
 hargav Bhatt).\n\n\nii) A new "relative" variant of perverse sheaves (join
 t work with Peter Scholze).\n\n\nIf time permits\, I'll mention some tanta
 lizing open problems in these directions.\n
LOCATION:https://researchseminars.org/talk/UMDANTFALL2021/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sug Woo Shin (UC Berkeley)
DTSTART:20211129T190000Z
DTEND:20211129T200000Z
DTSTAMP:20260422T212933Z
UID:UMDANTFALL2021/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMDANTFALL20
 21/6/">Stable trace formula for Shimura varieties of abelian type\, III</a
 >\nby Sug Woo Shin (UC Berkeley) as part of University of Maryland Algebra
 -Number Theory Seminar Fall 2021\n\nLecture held in Hybrid\, Kirwan Hall 3
 206.\n\nAbstract\nIn a recent paper with Mark Kisin and Yihang Zhu\, we pr
 oved the stable trace formula for Shimura varieties of abelian type. (This
  was the subject of Zhu’s talks in early October.) We will discuss appli
 cations of this formula. After a broad introduction to such applications\,
  we will specialize to the problem of describing the cohomology of Shimura
  varieties (joint work with Kisin and Zhu).\n
LOCATION:https://researchseminars.org/talk/UMDANTFALL2021/6/
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