Time：June 19, Wednesday, 16:00-17:00

Venue: Lecture Hall

Abstract: The Gan-Gross-Prasad (GGP) conjecture studies a family of restriction problems for classical groups and proposes precise answers to these problems using the local and global Langlands correspondences. It also has a twisted variant in the equal-rank Fourier-Jacobi case, which is called the twisted Gan-Gross-Prasad conjecture. In this talk, I will report my progress on the local twisted GGP conjecture for tempered representations in (GL(V),U(V)-case. 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 of a discrete series representation to prove the statement. Moreover, I will propose a geometric multiplicity formula for the local twisted GGP period and necessary ingredients to prove it.