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UID:6c9c0afaa4eeea53f8a321434c68dc30
CATEGORIES:Special Colloquium
CREATED:20221205T161939
SUMMARY:Langlands duality and higher traces
LOCATION:Zoom
DESCRIPTION:Abstract: A central theme in arithmetic geometry over finite fields is the 
 passage from geometric invariants to arithmetic information by taking the t
 race of Frobenius. I will describe a higher version of this procedure with 
 a particular focus on applications to the Langlands correspondence over fun
 ction fields. In this case, this procedure relates the geometric Langlands 
 correspondence with the classical one. Specifically, we obtain that the spa
 ce of automorphic functions is the categorical trace (aka Hochschild homolo
 gy) of Frobenius acting on an appropriate version of the automorphic catego
 ry. This leads to a localization of the space of automorphic functions on a
  moduli space of Langlands parameters, giving a refinement of V. Lafforgue'
 s spectral decomposition. This is based on joint works with Arinkin, Gaitsg
 ory, Kazhdan, Raskin, and Varshavsky.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="background: white;"><strong>Abstract:&nbsp;</strong>A central the
 me in arithmetic geometry over finite fields is the passage from geometric 
 invariants to arithmetic information by taking the trace of Frobenius. I wi
 ll describe a higher version of this procedure with a particular focus on a
 pplications to the Langlands correspondence over function fields. In this c
 ase, this procedure relates the geometric Langlands correspondence with the
  classical one. Specifically, we obtain that the space of automorphic funct
 ions is the categorical trace (aka Hochschild homology) of Frobenius acting
  on an appropriate version of the automorphic category. This leads to a loc
 alization of the space of automorphic functions on a moduli space of Langla
 nds parameters, giving a refinement of V. Lafforgue's spectral decompositio
 n. This is based on joint works with Arinkin, Gaitsgory, Kazhdan, Raskin, a
 nd Varshavsky.</p>
CONTACT:Nikita Rozenblyum (University of Chicago)
DTSTAMP:20260830T041905
DTSTART;TZID=America/New_York:20221205T140000
DTEND;TZID=America/New_York:20221205T150000
SEQUENCE:0
TRANSP:OPAQUE
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