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SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART:20211007T160000Z
DTEND:20211007T172000Z
DTSTAMP:20260423T021221Z
UID:RAMpAGe/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/51/"
 >Bun_G minicourse:  Local Langlands</a>\nby Tasho Kaletha (University of M
 ichigan) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
 n\nAbstract\nThis talk is the second part of a six-part series "$\\mathrm{
 Bun}_G$\, Shtukas\, and the Local Langlands Program"\, held Tuesdays and T
 hursdays between 5 and 21 October\, 2021.\n\nRecordings and slides will ap
 pear here:  https://sites.google.com/view/rampageseminar/home\n\nSeries ab
 stract:  The recent manuscript of Fargues-Scholze aims to "geometrize" the
  Langlands program for a p-adic group $G$\, by relating the players in tha
 t story to the stack $\\mathrm{Bun}_G$.  Following a strategy of V. Laffor
 gue\, the main result of [FS] is the construction of an L-parameter attach
 ed to a smooth irreducible representation of $G$.\n\nThe goal of this seri
 es is to review the main ideas of this work\, and to discuss two related r
 esults:  progress on the Kottwitz conjecture for local shtuka spaces by Ha
 nsen-Kaletha-Weinstein\,  and the construction of eigensheaves on $\\mathr
 m{Bun}_G$ when $G=\\mathrm{GL}_n$. \n\nTalk abstract: We will review some 
 representation-theoretic inputs to HKW. We’ll begin with reviewing the s
 tatements of the basic and refined local Langlands correspondence and the 
 status of their proofs. We will then define the relative position of two m
 embers of a compound L-packet\, which is an input to the Kottwitz conjectu
 re\, and the relative position of two regular semi-simple elements in inne
 r forms. Based on the latter\, we will define a Hecke transfer operator th
 at transfers conjugation-invariant functions between inner forms\, and dis
 cuss its effect on characters of supercuspidal representations.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/51/
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