I completed my DPhil in 2013 at the University of Oxford under the supervision of David Craven and Michael Collins. From 2013-2019 I was a Heilbronn Fellow first at the University of Bristol and then at the University of Leicester.
I am interested in interactions between algebraic topology group theory representation theory and combinatorics. Currently I am interested in using homotopy theory to develop a modular representation theory for spetses and related structures.
(0) The principal block of a $\ZZ_\ell$-spets and Yokonuma type algebras arXiv: 2106.14499 (joint with Radha Kessar and Gunter Malle) (submitted)
Weight conjectures for $\ell$-compact groups and spetses arXiv: 2008.07213 (joint with Radha Kessar and Gunter Malle) (submitted)
Weights in a Benson--Solomon block arXiv: 1712.02826 (joint with Justin Lynd) (submitted)
A $2$-compact group as a spets arXiv: 1906.00898 Exper. Math. (to appear)
Algorithms for fusion systems with applications to $p$ -groups of small order (joint with Chris Parker) J. Math. Comp. (2021)
Weight conjectures for fusion systems Adv. Math. 357 (2019), 1-40 (joint with Radha Kessar, Markus Linckelmann and Justin Lynd)
Fusion systems on maximal class $3$-groups of rank two revisited, Proc. Amer. Math. Soc. 147 (2019), 3773-3786 (joint with Chris Parker)
Fusion systems over a Sylow $p$-subgroup of $G_2(p)$ Math. Z. 289 (2018), 629-662 (joint with Chris Parker)
The cycle polynomial of a permutation group Electron. J. Comb, Volume 25, Issue 1 (2018) (joint with Peter Cameron)
Reduced fusion systems over $p$-groups with abelian subgroup of index $p$: II Adv. Math 322 (2017), 201-268 (joint with David Craven and Bob Oliver)
Conway's groupoid and its relatives Contemporary Mathematics Volume 694, 2017 in honour of John H. Conway (joint with Nick Gill, Neil Gillespie and Cheryl Praeger)
Tournaments, 4-uniform hypergraphs, and an exact extremal result J. Comb. Theory, Series B, 126 (2017) 114-136 (joint with Karen Gunderson).
Local structure of finite groups and more generally fusion systems; related topics in homotopy theory such as classifying spaces homotopical group theory compact Lie and p-compact groups; representations of groups (ordinary and modular) and finite dimensional algebras especially Iwahori-Hecke algebras and their generalisations; combinatorics relating to all of the above areas.
MA1114 Linear Algebra
MA2510 Investigations in Mathematics
MA3511 Communicating Mathematics
MA3142/MA4142 Representation Theory
Representations of Finite Groups Oberwolfach April 2023
Groups representations and applications: new perspectives INI Cambridge May-July 2022
Workshop on Homotopy Theory and Group Theory (IRP Higher Homotopical Structures) CRM Workshop Barcelona July 05-09 2021
CanaDAM 2021 Online May 25-28 2021
Groups representations and applications: new perspectives INI Cambridge March 01-14 2020
Groups and Geometries BIRS Banff August 25-30 2019
Classifying spaces of finite groups of Lie type Copenhagen July 2019
Representations of Finite Groups Oberwolfach March 2019
Group representation theory and applications MSRI Berkeley March 2018
Number theory and cryptography