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SUMMARY:Twisted orbital integrals and irreducible components of affine Del
 igne-Lusztig varieties - Rong Zhou (Imperial College London)
DTSTART:20200204T143000Z
DTEND:20200204T153000Z
UID:TALK136873@talks.cam.ac.uk
CONTACT:Jessica Fintzen
DESCRIPTION:Affine Deligne-Lusztig varieties (ADLV) naturally arise in the
  study of Shimura varieties and Rapoport-Zink spaces\; their irreducible c
 omponents give rise to an interesting class of cycles on the special fiber
  of Shimura varieties. In a joint work with Y. Zhu\, we give a description
  of the top-dimensional irreducible components of ADLV’s modulo the acti
 on of a natural symmetry group\, verifying a conjecture of M. Chen and X. 
 Zhu. In a work in progress with X. He and Y. Zhu\, we use the previous res
 ult to obtain a description of the irreducible components of the basic loc
 us of certain Shimura varieties in terms of a class set for an inner form 
 of the structure group\, generalizing classical results of Deuring and Ser
 re. A key input for our approach is an analysis of certain twisted orbital
  integrals using techniques from local harmonic analysis.\n\n
LOCATION:MR13
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