# Matthew Spencer

I'm a final year Ph.D. student under the supervision of Alex Bartel. My area of interest is primarily representation theory, and its applications to number theory and other areas of mathematics.

Specifically, I'm interested in relations between permutation modules , and how these relations can give non-trivial information about certain number theoretic objects. Over the course of my Ph.D. I have classified relations between \$\mathbb{F}_p[G]\$ permutation modules, both with and without semisimplification. In order to tackle these questions, I study maps between Green functors and their kernels, specifically the unique morphism from the Burnside functor to any Green functor.

For those who are interested, my CV is here: .

Papers:

Currently, I also have a paper in preparation:

Relations between permutation representations in positive characteristic (joint with Alex Bartel). - In this paper we will classify the structure of the kernel of the map from the Burnside ring of a finite group \$G\$ to the ring of \$\mathbb{F}_p[G]\$-modules. For all soluble groups; save for one family, we give explicit generators of the kernel.

I can be reached at MdotJdotSpenceratuniversityname.ac.uk .