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SUMMARY:Zhilin Luo (Minnesota)
DTSTART:20201211T153000Z
DTEND:20201211T170000Z
DTSTAMP:20260423T024517Z
UID:CAFAS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAFAS/13/">A
  local trace formula for the local Gan-Gross-Prasad conjecture for special
  orthogonal groups</a>\nby Zhilin Luo (Minnesota) as part of Columbia Auto
 morphic Forms and Arithmetic Seminar\n\n\nAbstract\nThe local Gan-Gross-Pr
 asad conjecture studies the restriction and branching problems for represe
 ntations of classical and metaplectic groups. In this talk\, I will talk a
 bout my proof for the tempered part of the local Gan-Gross-Prasad conjectu
 re (multiplicity one in Vogan packets) for special orthogonal groups over 
 any local fields of characteristic zero\, which combines the work of Walds
 purger (for the tempered part of the conjecture for special orthogonal gro
 ups over $p$-adic fields) and Beuzart-Plessis (for the tempered part of th
 e conjecture for unitary groups over real field) in a non-trivial way. In 
 the proof\, an indispensable result which is also of independent interest 
 is a formula expressing the regular nilpotent germs of quasi-split reducti
 ve Lie algebras over any local fields of characteristic zero via endoscopi
 c invariants\, which was previously proved by Shelstad over $p$-adic field
 s. We also relate the formula with the Kostant's sections.\n
LOCATION:https://researchseminars.org/talk/CAFAS/13/
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