The Gan-Gross-Prasad conjectures for unitary groups

The Gan-Gross-Prasad conjectures connect two central themes in the theory of automorphic forms: the study of branching laws in the representation theory of classical (real or p-adic) Lie groups, and the relation between automorphic periods and special values of L functions. In this introductory talk, I will explain how a celebrated result of Waldspurger unites these two questions for GL2. I will then describe the generalization proposed by Gan, Gross and Prasad in the case of unitary groups, and discuss recent progress.