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SUMMARY:Arghya Sadhukhan (Maryland)
DTSTART:20230112T220000Z
DTEND:20230112T230000Z
DTSTAMP:20260423T022809Z
UID:UCSD_NTS/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/86/
 ">Understanding the dimension of some (union of) affine Deligne-Lusztig va
 rieties via the quantum Bruhat graph</a>\nby Arghya Sadhukhan (Maryland) a
 s part of UCSD number theory seminar\n\nLecture held in APM 6402 and onlin
 e.\n\nAbstract\nThe study of affine Deligne-Lusztig varieties (ADLVs) $X_w
 (b)$ and their certain union $X(\\mu\,b)$ has been crucial in understandin
 g mod-$p$ reduction of Shimura varieties\; for instance\, precise informat
 ion about the connected components of ADLVs (in the hyperspecial level) ha
 s proved to be useful in Kisin's proof of the Langlands-Rapoport conjectur
 e. On the other hand\, first introduced in the context of enumerative geom
 etry to describe the quantum cohomology ring of complex flag varieties\, q
 uantum Bruhat graphs have found recent applications in solving certain pro
 blems on the ADLVs. I will survey such developments and report on my work 
 surrounding a dimension formula for $X(\\mu\,b)$ in the quasi-split case\,
  as well as some partial description of the dimension and top-dimensional 
 irreducible components in the non quasi-split case.\n\npre-talk at 1:20pm\
 n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/86/
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