Algebra/Topology seminar

Speaker: Luca Pol

Title: Representation stability and outer automorphism groups

Abstract: In this talk I will present a framework for studying families of representations of the outer automorphism groups indexed on a collection of finite groups U. One can encode this large amount of data into a convenient abelian category AU which generalizes the category of VI-modules appearing in the representation theory of the finite general linear groups. Inspired by work of Church--Ellenberg--Farb, I will discuss for which choices of U the abelian category is locally noetherian and deduce analogues of central stability and representation stability results in this setting. As an application, I will show that some invariants coming from rational global homotopy theory exhibit such a stable behavior.