Research

Preprints of all of my mathematics papers can be found on the arXiv.

Submitted papers

• The binary actions of simple groups of Lie type of characteristic 2 (with Pierre Guillot and Martin Liebeck)
• The binary actions of simple groups with a single conjugacy class of involutions (with Pierre Guillot)
• The binary actions of alternating groups (with Pierre Guillot)

Published mathematics papers

1. Nilpotent covers of dihedral groups (with Kimeu Arphaxad Ngwava), to appear in Ars Combinatoria.
2. A generalization of Szep’s conjecture for almost simple groups (with Michael Guidici and Pablo Spiga), Vietnam J. Math. 52, No. 2, 325–259 (2024)
3. Irredundant bases for finite groups of Lie type (with Martin Liebeck), Pacific J. Math. 322, No. 2, 281–200 (2023).
4. Large minimal invariable generating sets in the finite symmetric groups (with Daniele Garzoni),Israel J. Math. 255, No. 2, 581–598 (2023).
5. On the number of conjugacy classes of a primitive permutation group (with Daniele Garzoni), Proc. R. Soc. Edinb., Sect. A, Math. Sect. A, Math. 153, No. 1, 115–136 (2023).
6. Nilpotent covers of symmetric groups (with Kimeu Arphaxad Ngwava and Ian Short), Bulletin of the Belgian Mathematical Society – Simon Stevin 29, No. 2, 249–256 (2022).
7. Cherlin’s conjecture on finite primitive binary permutation groups (with Martin Liebeck and Pablo Spiga), Lecture Notes in Mathematics, Vol 2302, Springer, 213p. 2022.
8. Statistics for S_n acting on k-sets (with Bianca Loda), J. Algebra 607, Part A, 286-299 (2022).
9. On the height and relational complexity of a finite permutation group (with Bianca Loda and Pablo Spiga), Nagoya Math. J. 246, 372-411 (2022).
10. The character table of a sharply 5-transitive subgroup of the alternating group on 12 letters (with Sam Hughes), Int. J. Group Theory 10, No. 1, 11-30 (2021).
11. A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank (with Laszlo Pyber and Endre Szabo), Bull. LMS 52, No. 3, 464-471 (2020).
12. Binary groups: Alternating and classical groups (with Pablo Spiga), Amer. J. Math. 142, No. 1, 1-43 (2020).
13. Cherlin’s conjecture for almost simple groups of Lie rank 1 (with Francis Hunt and Pablo Spiga), Math. Proc. Camb. Philos. Soc. 167, No. 3, 417-435 (2019).
14. Conway’s groupoid and its relatives (with Neil Gillespie, Cheryl Praeger and Jason Semeraro), published in Finite Simple Groups: Thirty Years of the Atlas and Beyond. Vol. 694 Princeton, NJ : American Mathematical Society, 2017. (Contemporary Mathematics).
15. Conway groupoids, regular two-graphs and supersimple designs (with Neil Gillespie, Cheryl Praeger and Jason Semeraro), Sémin. Lothar. Comb. 79 (2017-2018), B79b, 24 p. (2018).
16. Cherlin’s conjecture for sporadic simple groups (with Francesca Dalla Volta and Pablo Spiga), Pac. J. Math. 297, No. 1, 47-66 (2018).
17. Conway groupoids and completely transitive codes (with Neil Gillespie and Jason Semeraro), Combinatorica 38, No. 2, 399-442 (2018).
18. Perfect commuting graphs (with John Britnell), J. Group Theory 20, No. 1, 71-102 (2017).
19. Quasirandom group actions, Forum of Mathematics (Sigma) 4, Article ID e24, 35 p. (2016).
20. Abelian covers of alternating groups (with Daniel Barrantes and Jeremias Ramirez), Archiv der Mathematik. 107, No. 2, 135-150 (2016).
21. On a conjecture of Degos, Cah. Topol. Géom. Différ. Catég. 57, No. 3, 229-237 (2016). (Details of erratum.)
22. Generating groups using hypergraphs (with Neil Gillespie, Tony Nixon and Jason Semeraro), Quarterly Journal of Mathematics, (2016) 67 (1), 29-52.
23. Transitive projective planes and insoluble groups. Transactions of the American Mathematical Society 368 (2016), 3017-3057.
24. Nilpotent covers and non-nilpotent subsets of finite groups of Lie type (with Azizollah Azad and John Britnell). Forum Mathematicum 27 (2015), 3745-3782.
25. On growth in an abstract plane (with Harald Helfgott and Misha Rudnev), Proceedings of the American Mathematical Society 143 no. 8 (2015), 3593-3602.
26. Growth in solvable subgroups of GL_r(Z/pZ) (with Harald Helfgott), Mathematische Annalen 360 (2014), no. 1-2, 157-208.
27. On the product decomposition conjecture for finite simple groups (with Laszlo Pyber, Ian Short and Endre Szabo), Groups, Geometry, and Dynamics, 7 (2013), no.4, 867–882.
28. Orientably regular maps with Euler characteristic divisible by few primes. Journal of the London Mathematical Society, 88 (2013), no.1, 118–136.
29. Conjugacy in Thompson’s group F (with Ian Short), Proceedings of the American Mathematical Society, 141 (2013)1529–1538.
30. (2,m,n)-groups with Euler characteristic equal to -2^as^b. Electronic Journal of Combinatorics, 20 (2013), no. 3, R8.
31. A note on the Weiss conjecture. Journal of the Australian Mathematical Society, 95 (2013), no.3 356-361.
32. Bounds on the diameter of Cayley graphs of the symmetric group(with John Bamberg, Thomas P. Hayes, Harald Helfgott, Akos Seress and Pablo Spiga), Journal of Algebraic Combinatorics 40 (2014), no. 1, 1-22.
33. Real and strongly real classes in SL(n,q) (with Anupam Singh), Journal of Group Theory, 14 (2011), no.3, pp. 437–459.
34. Real and strongly real classes in PGL(n,q) and quasi-simple covers of PSL(n,q) (with Anupam Singh), Journal of Group Theory, 14 (2011), no.3, 461–489.
35. Growth of small generating sets in SL(n,pZ/Z) (with Harald Helfgott), International Mathematics Research Notices, 18 (2011), 4226–4251.
36. Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line (with Ian Short), Aequationes Mathematicae, 79(2010), no.1-2, 23–37.
37. Reversibility in the group of homeomorphisms of the circle (with Anthony G. O’Farrell and Ian Short), Bulletin of the London Mathematical Society, 41 (2009), no.5, 885–897.
38. Large dimensional classical groups and linear spaces (with Alan Camina and Alex Zalesski), Bulletin of the Belgian Mathematical Society (Simon Stevin), 15 (2008), no.4, 705–731.
39. Transitive projective planes, Advances in Geometry, 7 (2007), no.4, 475–528.
40. PSL(3,q) and line-transitive linear spaces, Beiträge zur Algebra und Geometrie, 48 (2007), no.2, 591–620.
41. Polar spaces and embeddings of classical groups, New Zealand Journal of Mathematics, 36 (2007), 175–184.
42. Linear spaces with significant characteristic prime, Innovations in Incidence Geometry, 3 (2006), 109–119.
43. Nilpotent Singer groups, Electronic Journal of Combinatorics, 13 (2006), no.1, R94.

Published papers on deliberative democracy

1. Can we do inclusive politics in urgent times? (with Brett Hennig and Thomas Lord), published online 9 March 2024. Not yet in print.

Other activity

• I wrote this note in response to this MathOverflow question. Shortly afterwards I realised that Mohammad Reza Darafsheh had beaten me to it, so this note is unlikely to be published.
• Marcus Hum, Dömötör Pálvölgyi and I answered the MathOverflow question Is there always a maximum anti-rectangle with a corner square?. Our answer was cited in this economics(!) paper.
• A letter in the Guardian;
• An article on free journals in mathematics. The article gives some of the reasons why I, and many others, choose to publish in low-cost or free journals.

I am a reviewer for Zentralblatt, MathSciNet and the Newsletter of the London Maths. Soc. I have refereed articles for many different journals, but I won’t referee for Elsevier.

Until recently (2023), I was a member of the European Mathematical Society’s Committee for Developing Countries.