I am a Heilbronn Research Fellow at the University of Manchester. Broadly, I study group theory.
I am currently interested in local group theory, specifically through the lens of saturated fusion systems over p-groups and their interactions with group amalgams. In fusion systems, my current research focuses on recognizing the p-fusion categories of simple groups of Lie type from prescribed local actions.
Alongside this, I am interested in exotic fusion systems at odd primes, and the applications of fusion systems to representation theory and homotopy theory.
A PDF copy of my CV is here .
- Fusion Systems
- Amalgams of Finite Groups
- Finite Local Group Theory
PhD in Pure Mathematics, 2022
University of Birmingham
MASt in Mathematical Sciences, 2017
University of Warwick
BSc in Mathematics, 2016
University of Glasgow
Publications
Books/Monographs
- van Beek, M. Rank 2 Amalgams and Fusion Systems. Lecture Notes in Mathematics. (2024).
Published Papers
van Beek, M. Saturated Fusion Systems on Sylow $p$-subgroups of Rank $2$ Simple Groups of Lie Type. Forum of Mathematics, Sigma. (2024).
van Beek, M. Fusion Systems on a Sylow $p$-subgroup of $G_2(p^n)$ or $PSU_4(p^n)$. Journal of Algebra. (2023).
Submitted Papers
Grazian, V. & Parker, C. & Semeraro, J. & van Beek, M. Fusion systems related to polynomial representations of $\mathrm{SL}_2(q)$. (2025).
Parker, C. & van Beek, M. Lifting Polynomial Representations of $\mathrm{SL}_2(p^r)$ from $\mathbb{F}_p$ to $\mathbb{Z}/p^s\mathbb{Z}$. (2024).
van Beek, M. Fusion Systems and Simple Groups With Class Two Sylow $p$-subgroups. (2024).
van Beek, M. Exotic Fusion Systems Related to Sporadic Simple Groups. (2022).
Employment
Teaching
In February 2024, I taught a short postgraduate course titled “Topics in Finite $p$-groups.” Here are the notes and problem sheets:
Lecture Notes
Problem Sheet 1
Problem Sheet 2
Problem Sheet 3
Problem Sheet 4
Any suggestions or corrections would be greatly appreciated!
Contact
- martin.vanbeek@manchester.ac.uk
- Alan Turing Building, University of Manchester, Manchester, M13 9PL