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SUMMARY:Jonathan Wang (MIT Mathematics)
DTSTART:20200923T203000Z
DTEND:20200923T213000Z
DTSTAMP:20260423T021033Z
UID:MITLie/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/9/">S
 pherical varieties\, L-functions\, and crystal bases</a>\nby Jonathan Wang
  (MIT Mathematics) as part of MIT Lie groups seminar\n\nLecture held in 2-
 142.\n\nAbstract\nThe program of Sakellaridis and Venkatesh proposes a uni
 fied framework to study integral representations of L-functions through th
 e lens of spherical varieties. For X an affine spherical variety\, the (hy
 pothetical) IC complex of the infinite-dimensional formal arc space of X i
 s conjecturally related to special values of local unramified L-functions.
  We formulate this relation precisely using a new conjectural geometric co
 nstruction of the crystal basis of a finite-dimensional representation (de
 termined by X) of the dual group. We prove these conjectures for a large c
 lass of spherical varieties. This is joint work with Yiannis Sakellaridis.
 \n
LOCATION:https://researchseminars.org/talk/MITLie/9/
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