Speaker: Sahana Balasubramanya
Title: The semi simple theory of acylindricity in higher rank
Abstract: In this talk, I will discuss forthcoming work with T.Fernos that explores the theory for countable groups acting (AU-) acylindrically on products of hyperbolic spaces. This theory draws inspiration from the theory of S-arithmetic lattices in linear algebraic groups as well as acylindrical actions on a single hyperbolic space (rank-1 case). We reprove and extend many results about acylindricity from rank-1 to higher rank, explore elementary subgroups in higher rank and prove results akin to the Tits alternative. We also give a partial answer to a recent conjecture of Sela concerning outer automorphism groups in this setting.