The twisted Gan-Gross-Prasad conjecture over finite fields and p-adic fields
Date(s) : 05/12/2023 iCal
14h00 - 15h00
The Gan-Gross-Prasad (GGP) conjecture studies a family of restriction problems for classical groups and proposes precised answers to these problems using the local and global Langlands correspondences. It also has a twisted variant in the Fourier-Jacobi case, which is called the twisted Gan-Gross-Prasad conjecture. In the first 15 minutes, I will present my progress on the twisted GGP problem over finite fields, which is motivated by the works of Reeder in Bessel case and Liu-Ma-Shi in Fourier-Jacobi case. In the remaining time, I will go through my work-in-progress on the local twisted GGP conjecture for tempered representations of general linear groups. The strategy is to adapt Waldspurger and Beuzart-Plessis’s method to develop a local relative trace formula as well as a twisted trace formula and compare their elliptic parts. Although the geometric sides of both trace formulae have not been developed, one can use a partial comparison and an instance for the Steinberg representation to prove the statement.
Emplacement
I2M Luminy - Ancienne BU, Salle Séminaire2 (RdC)
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