BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Yihang Zhu (University of Maryland)
DTSTART:20211004T180000Z
DTEND:20211004T190000Z
DTSTAMP:20260404T111006Z
UID:UMDANTFALL2021/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UMDAN
 TFALL2021/1/">Stable trace formula for Shimura varieties of abelian type\,
  I</a>\nby Yihang Zhu (University of Maryland) as part of University of Ma
 ryland 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.um
 d.edu/~yhzhu/KSZ.pdf) (The third talk will be given by Shin.)\n\nWe consid
 er the alternating trace of a Hecke operator away from p and a Frobenius p
 ower at p acting on the compact support cohomology of a Shimura variety of
  abelian 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 endosco
 pic groups with respect to well-chosen test functions\, proving a conjectu
 re of Kottwitz.\n\nIn the first talk\, we give some historical background\
 , state the problem\, and discuss our strategy of reducing the result to a
  form of the Langlands-Rapoport Conjecture where certain "controlled twist
 s" are allowed. This form of Langlands-Rapoport strengthens what was prove
 d in earlier work of Kisin.\n
LOCATION:https://stable.researchseminars.org/talk/UMDANTFALL2021/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihang Zhu (University of Maryland)
DTSTART:20211006T180000Z
DTEND:20211006T190000Z
DTSTAMP:20260404T111006Z
UID:UMDANTFALL2021/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UMDAN
 TFALL2021/2/">Stable trace formula for Shimura varieties of abelian type\,
  II</a>\nby Yihang Zhu (University of Maryland) as part of University of M
 aryland 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 cons
 ider 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 abelian type with hyperspecial level at p. We show that this is equal t
 o the sum of the elliptic parts of the stable trace formulas for the endos
 copic groups with respect to well-chosen test functions\, proving a conjec
 ture of Kottwitz.  \n\nIn the second talk\, we discuss some ingredients in
  the proof of the Langlands-Rapoport-tau Conjecture introduced in the firs
 t talk. In the case of Hodge type\, we use Breuil-Kisin modules and a rece
 nt purity result of Ansch\\"utz to construct certain "non-standard" lattic
 es in the rational Dieudonn\\'e modules of the reductions of special point
 s. These lattices serve as "marking points" that play a key role in the pr
 oof.\n
LOCATION:https://stable.researchseminars.org/talk/UMDANTFALL2021/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ananth Shankar (University of Wisconsin\, Madison)
DTSTART:20211026T180000Z
DTEND:20211026T190000Z
DTSTAMP:20260404T111006Z
UID:UMDANTFALL2021/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UMDAN
 TFALL2021/3/">Canonical heights on Shimura varieties and the Andre-Oort co
 njecture</a>\nby Ananth Shankar (University of Wisconsin\, Madison) as par
 t of University of Maryland Algebra-Number Theory Seminar Fall 2021\n\n\nA
 bstract\nLet S be a Shimura variety. The Andre-Oort conjecture posits that
  the Zariski closure of special points must be a sub Shimura subvariety of
  S. The Andre-Oort conjecture for A_g (the moduli space of principally pol
 arized Abelian varieties) — and therefore its sub Shimura varieties — 
 was proved by Jacob Tsimerman. However\, this conjecture was unknown for S
 himura varieties without a moduli interpretation. I will describe joint wo
 rk with Jonathan Pila and Jacob Tsimerman (with an appendix by Esnault-Gro
 echenig) where we prove the Andre Oort conjecture in full generality.\n
LOCATION:https://stable.researchseminars.org/talk/UMDANTFALL2021/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (Max-Planck Institut Bonn)
DTSTART:20211108T190000Z
DTEND:20211108T200000Z
DTSTAMP:20260404T111006Z
UID:UMDANTFALL2021/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UMDAN
 TFALL2021/4/">On the Kottwitz conjecture for local shtuka spaces</a>\nby D
 avid Hansen (Max-Planck Institut Bonn) as part of University of Maryland A
 lgebra-Number Theory Seminar Fall 2021\n\n\nAbstract\nThe cohomology of lo
 cal Shimura varieties\, and of more general spaces of local shtukas\, is o
 f fundamental interest in the Langlands program. On the one hand\, it is s
 upposed 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 pr
 oved the first general results towards the Kottwitz conjecture\, which pre
 dicts how supercuspidal L-packets contribute to the cohomology of local sh
 tuka spaces. I will review this story\, and give some overview of the idea
 s which enter into our proof. The key idea in our argument - namely\, that
  the Kottwitz conjecture should follow from some form of the Lefschetz-Ver
 dier fixed point formula - was already formulated by Michael Harris in the
  '90s. However\, executing this idea brings substantial technical challeng
 es. I will try to emphasize the new ingredients which allow us to implemen
 t this idea in full generality.\n
LOCATION:https://stable.researchseminars.org/talk/UMDANTFALL2021/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (Max-Planck Institut Bonn)
DTSTART:20211110T190000Z
DTEND:20211110T200000Z
DTSTAMP:20260404T111006Z
UID:UMDANTFALL2021/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UMDAN
 TFALL2021/5/">Recent developments in etale cohomology</a>\nby David Hansen
  (Max-Planck Institut Bonn) as part of University of Maryland Algebra-Numb
 er Theory Seminar Fall 2021\n\n\nAbstract\nI'll talk about some recent fou
 ndational developments in etale cohomology:\n\n\ni) A flexible six-functor
  formalism for "Zariski-constructible" sheaves on rigid spaces (joint work
  with Bhargav Bhatt).\n\n\nii) A new "relative" variant of perverse sheave
 s (joint work with Peter Scholze).\n\n\nIf time permits\, I'll mention som
 e tantalizing open problems in these directions.\n
LOCATION:https://stable.researchseminars.org/talk/UMDANTFALL2021/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sug Woo Shin (UC Berkeley)
DTSTART:20211129T190000Z
DTEND:20211129T200000Z
DTSTAMP:20260404T111006Z
UID:UMDANTFALL2021/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UMDAN
 TFALL2021/6/">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 3206.\n\nAbstract\nIn a recent paper with Mark Kisin and Yihang Zhu\
 , we proved the stable trace formula for Shimura varieties of abelian type
 . (This was the subject of Zhu’s talks in early October.) We will discus
 s applications of this formula. After a broad introduction to such applica
 tions\, we will specialize to the problem of describing the cohomology of 
 Shimura varieties (joint work with Kisin and Zhu).\n
LOCATION:https://stable.researchseminars.org/talk/UMDANTFALL2021/6/
END:VEVENT
END:VCALENDAR