Workshop on Topology: Identifying Order in Complex Systems

The Picard group of the stable module category of a finite group plays a role in many parts of modular representation theory. It was calculated when the group is an abelian $p$-group, by pioneering work of Dade in the 1970's, and a classification for all $p$-groups was obtained by Carlson-Thevenaz in the early 2000's in a series of works. In my talk I'll explain how to use methods from homotopy theory and higher algebra to describe this Picard group for an arbitrary finite group $G$. Part of this talk is joint work with Tobias Barthel and Joshua Hunt.