Families of branching laws and their arithmetic applications

Abstract: The branching laws of certain special pairs of algebraic groups $H \to G$ are related to the $L$-functions of automorphic representations via the theory of period integrals, made concrete by the conjectures of Gan--Gross--Prasad and Ichino--Ikeda. On the algebraic side, one can use branching laws for highest weight representations to construct cohomological avatars of automorphic period integrals in the cohomology of Shimura varieties. These classes are related to $p$-adic $L$-functions and Euler systems, both of which have applications to important arithmetic conjectures such as the Bloch--Kato conjectures. I will explain how one constructs such avatars and will describe work of myself and Loeffler--Zerbes on varying these classes in $p$-adic families.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.