Matthew Spencer
I recently completed my Ph.D. 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:
- A note on Green functors with inflation (joint with Alex Bartel) - This paper serves as a workhorse where we develop the underlying techniques used to analyse the kernel of maps between Green functors. (J.Algebra vol 483 pages 230-244).
- Brauer relations for finite groups in the ring of semisimplified modular representations - In this paper we completely classify the structure of the kernel of the map from the Burnside ring of a finite group $G$ to the Grothendieck ring of $\mathbb{F}_p[G]$ modules. (submitted).
- 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 .