BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Tony Feng (UC Berkeley)
DTSTART:20251118T220000Z
DTEND:20251118T230000Z
DTSTAMP:20260419T151654Z
UID:BC-MIT/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BC-MIT/26/">
 Mirror symmetry and the Breuil—Mezard Conjecture: an update</a>\nby Tony
  Feng (UC Berkeley) as part of BC-MIT number theory seminar\n\nLecture hel
 d in 2-449 at MIT.\n\nAbstract\nThe Breuil—Mezard Conjecture predicts a 
 precise indexing of cycles in moduli spaces of local Galois representation
 s by modular representations of finite groups of Lie type. A couple years 
 ago\, Bao Le Hung and I introduced a new approach to the Breuil—Mezard C
 onjecture based on a connection to an instance of mirror symmetry\, which 
 in that instance predicts a precise indexing of Lagrangians in a symplecti
 c variety by representations of a quantum group. Recently\, we used this t
 o prove the Breuil—Mezard Conjecture in the generic range for arbitrary 
 unramified groups\, including exceptional groups. My intent is to review t
 his and also work-in-progress with Le Hung and Zhongyipan Lin\, which aims
  to extend the result to ramified groups. The key new aspect of the ramifi
 ed case is a nascent theory of "Spectral Langlands functoriality"\, an ana
 logue of Langlands functoriality for the spectral (i.e.\, "Galois") side o
 f the Langlands correspondence.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/26/
END:VEVENT
END:VCALENDAR