Abstract:

Let G be a group and let H be a subgroup of G. The branching problem is to decompose representations of G restricted to H. This talk will begin with compact groups and then discuss some recent problems for other reductive groups such as Gan-Gross-Prasad conjectures and homological variations. Connections to number theory, Hecke algebras and quantum groups will also be discussed. Results presented in the talk are joint with Gordan Savin.