Title: The local theta correspondence and functoriality Abstract: In a letter to Howe, Langlands conjectured that the local theta correspondence is an instance of Langlands functoriality, e.g., it should preserve L-packets. Unfortunately, this was false. As a remedy, Adams conjectured that instead of L-packets, the local theta correspondence should preserve Arthur packets. Mœglin showed that […]

Title: Relative Satake isomorphism and Euler systems Abstract: Starting from the inversion formula for the relative Satake isomorphism due to Sakellaridis, we observe a simple additional divisibility property. We will then explain how this gives a computation-free construction of Euler systems in some settings. This is joint work with Li Cai and Yangyu Fan.

Title: On the Gan-Gross-Prasad conjecture for unitary groups Abstract: The Gan-Gross-Prasad conjecture stipulates the existence of relations between the central values of certain L-functions and some automorphic periods on classical groups. It can be seen as a higher rank generalization of a famous formula of Waldspurger for toric periods on GL(2). In this talk, I […]

Title: Shimura Varieties and Eigensheaves Abstract: The cohomology of Shimura varieties is a fundamental object of study in algebraic number theory by virtue of the fact that it is the only known geometric realization of the global Langlands correspondence over number fields. Usually, the cohomology is computed through very delicate techniques involving the trace formula. […]