Heilbronn Research Fellow

Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

jpgs1@leicester.ac.uk

js13525@bristol.ac.uk

Office Tel: +44 (0)116 252 3892

About me

I completed my DPhil in 2013 at the University of Oxford under the supervision of David Craven and Michael Collins. From 2013-2016 I was a Heilbronn Fellow at the University of Bristol. I want to shed light on the precise relationships between exotic objects in group theory, representation theory and algebraic topology: fusion systems, spetses and $p$-compact groups, with the broad aim of understanding some of these.

From October 2019 I will be a Lecturer at the University of Leicester.

Research

A compendium of fusion systems over $p$-groups of small order (joint with Chris Parker) (in preparation)

A $2$-compact group as a spets arXiv: 1906.00898 (submitted)

Weights in a Benson--Solomon block arXiv: 1712.02826 (joint with Justin Lynd) (submitted)

Weight conjectures for fusion systems arXiv: 1810.01453 to appear in Adv. Math (joint with Radha Kessar, Markus Linckelmann and Justin Lynd)

Fusion systems on maximal class $3$-groups of rank two revisited arXiv: 1809.01957, to appear in Proc. AMS (joint with Chris Parker)

Fusion systems over a Sylow $p$-subgroup of $G_2(p)$ arXiv:1608.08399 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) arXiv: 1701.06954 (joint with Peter Cameron)

Conway groupoids and completely transitive codes arXiv:1410.4785 Combinatorica, 38 (2) (2018) 399-442| (joint with Nick Gill and Neil Gillespie)

Reduced fusion systems over $p$-groups with abelian subgroup of index $p$: IIAdv. Math 322 (2017), 201-268 arXiv:1606.05133 (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)

Conway groupoids, regular two-graphs and supersimple designs Séminaire Lotharingien de Combinatoire, Issue 79 (2017) arXiv:1510.06680 (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 arXiv:1509.03268 (joint with Karen Gunderson)

Generating groups using hypergraphs Quart. J. Math, 67 (1) (2016), 29-52 arXiv:1405.1701 (joint with Nick Gill, Neil Gillespie and Tony Nixon)

Bounding the number of hyperedges in friendship $r$-hypergraphs European J. Combinatorics 51 (2016), 125-134 arXiv:1412.5822 (joint with Karen Gunderson and Natasha Morrison)

Centralizers of normal subgroups and the $Z^*$-theorem J. Algebra 439 (2015), 511-514 arXiv:1411.1932 (joint with Ellen Henke)

Centralizers of subsystems of fusion systems J. Group Theory 18 (2015), 393-405 arXiv:1402.4981

Trees of fusion systems J. Algebra, 399 (2014), 1051-1072 arXiv:1211.6700

DPhil thesis (2013)

MPhil thesis (2009)

Useful Links

arXiv
Maths Genealogy Project
University of Leicester
BLOC
Terence Tao's blog
Tim Gower's blog
University of Bristol

Fun Stuff

Noughts and Crosses
Conway's Cosmological Theorem
M(13) demonstration
Finite simple group of order two
Quiver mutations in Java