PhD Defence Joshua Hunt

Title: Decompositions and obstructions for the stable module ∞-category

Abstract: I will discuss decompositions of ∞-categories: what they are, how we can construct them, and what they're useful for. In particular, I will show how we can construct three different types of decompositions of the stable module ∞-category of a finite group G (corresponding to the subgroup, centraliser, and normaliser decompositions of classifying spaces that were constructed by Dwyer), and apply the subgroup decomposition to help understand the group of endotrivial modules of G. The latter is joint work with Tobias Barthel and Jesper Grodal. I aim to make at least 70% of the talk accessible to a general audience!

You can also attend via Zoom.

Supervisor:

Prof. Jesper Grodal, Department of Mathematical Sciences, University of Copenhagen

Assessment committee:

• Prof. Jesper Michael Møller, Chair. Department of Mathematical Sciences.
• Prof. Stefan Schwede, University of Bonn
• Prof. Jon Carlson, University of Georgia