The Picard group of the stable module category of a finite group

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.