Title : Relative Langlands duality

Abstract : In the theory of automorphic representations, the periods play the role of automorphic quasi-invariant functionals over the space of automorphic representations. Under certain geometric conditions, they can be interpreted as integral representations of L-functions or equal to the special values of L-functions. Recently, D. Ben-Zvi, Y. Sakellaridis, and A. Venkatesh set up the general framework of relative Langlands duality to formulate a series of conjectures on such connections and their duality. In this talk, we will focus on the automorphic side of BZSV duality and investigate the strongly tempered cases. This talk is based on a series of joint works with Chen Wan and Zhengyu Mao at Rutgers—Newark.