# Research

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

## Submitted papers

1. Conway’s groupoid and its relatives (with Neil Gillespie, Cheryl Praeger and Jason Semeraro), to appear in the AMS Contemporary Mathematics Series volume in honour of John H. Conway.
2. Abelian covers of alternating groups (with Daniel Barrantes and Jeremias Ramirez), to appear in Archiv der Mathematik.
3. Perfect commuting graphs (with John Britnell), to appear in Journal of Group Theory.
4. Quasirandom group actions, to appear in Forum of Mathematics (Sigma).
5. (with Neil Gillespie and Jason Semeraro) Conway groupoids and completely transitive codes, to appear in Combinatorica.
6. On a conjecture of Degos, to appear in Cahiers de topologie et geometrie differentielle categoriques.
7. (with Neil Gillespie, Tony Nixon and Jason Semeraro) Generating groups using hypergraphs. Quarterly Journal of Mathematics, (2016) 67 (1), 29-52.
8. Transitive projective planes and insoluble groups. Transactions of the American Mathematical Society 368 (2016), 3017-3057.
9. (with Azizollah Azad and John Britnell) Nilpotent covers and non-nilpotent subsets of finite groups of Lie type. Forum Mathematicum 27 (2015), 3745-3782.
10. (with Harald Helfgott and Misha Rudnev). On growth in an abstract plane. Proceedings of the American Mathematical Society 143 no. 8 (2015), 3593-3602.
11. (with Harald Helfgott) Growth in solvable subgroups of ${\rm GL}_r({\mathbb Z}/p{\mathbb Z})$. Mathematische Annalen 360 (2014), no. 1-2, 157-208.
12. (with Laszlo Pyber, Ian Short and Endre Szabo). On the product decomposition conjecture for finite simple groups. Groups, Geometry, and Dynamics, 7 (2013), no.4, 867–882.
13. Orientably regular maps with Euler characteristic divisible by few primes. Journal of the London Mathematical Society, 88 (2013), no.1, 118–136.
14. (with Ian Short). Conjugacy in Thompson’s group $F$. Proceedings of the American Mathematical Society, 141 (2013)1529–1538.
15. (2,m,n)-groups with Euler characteristic equal to $-2^as^b$. Electronic Journal of Combinatorics, 20 (2013), no. 3, R8.
16. A note on the Weiss conjecture. Journal of the Australian Mathematical Society, 95 (2013), no.3 356-361.
17. (with John Bamberg, Thomas P. Hayes, Harald Helfgott, Akos Seress and Pablo Spiga). Bounds on the diameter of Cayley graphs of the symmetric group. Journal of Algebraic Combinatorics 40 (2014), no. 1, 1-22.
18. (with Anupam Singh). Real and strongly real classes in ${\rm SL}_n(q)$. Journal of Group Theory, 14 (2011), no.3, pp. 437–459.
19. (with Anupam Singh) Real and strongly real classes in ${\rm PGL}_n(q)$ and quasi-simple covers of ${\rm PSL}_n(q)$. Journal of Group Theory, 14 (2011), no.3, 461–489.
20. (with Harald Helfgott) Growth of small generating sets in ${\rm SL}_n({\mathbb Z}/p{\mathbb Z})$. International Mathematics Research Notices, 18 (2011), 4226–4251.
21. (with Ian Short) Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line. Aequationes Mathematicae, 79(2010), no.1-2, 23–37.
22. (with Anthony G. O’Farrell and Ian Short) Reversibility in the group of homeomorphisms of the circle. Bulletin of the London Mathematical Society, 41 (2009), no.5, 885–897.
23. (with Alan Camina and Alex Zalesski) Large dimensional classical groups and linear spaces. Bulletin of the Belgian Mathematical Society (Simon Stevin), 15 (2008), no.4, 705–731.
24. Transitive projective planes. Advances in Geometry, 7 (2007), no.4, 475–528.
25. PSL(3,q) and line-transitive linear spaces. Beiträge zur Algebra und Geometrie, 48 (2007), no.2, 591–620.
26. Polar spaces and embeddings of classical groups. New Zealand Journal of Mathematics, 36 (2007), 175–184.
27. Linear spaces with significant characteristic prime. Innovations in Incidence Geometry, 3 (2006), 109–119.
28. Nilpotent Singer groups. Electronic Journal of Combinatorics, 13 (2006), no.1, R94.

## Other activity

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.

I am an associate member of, and the webmaster for, the European Mathematical Society’s Commission for Developing Countries.

And finally, two talks that I’ve given at Banff: