# Research

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

## Submitted papers

- Cherlin’s conjecture for sporadic simple groups (with Francesca Dalla Volta and Pablo Spiga)
- Cherlin’s conjecture for almost simple groups of Lie rank 1 (with Francis Hunt and Pablo Spiga)
- Binary groups: Alternating and classical groups (with Pablo Spiga)
- Conway groupoids, regular two-graphs and supersimple designs (with Neil Gillespie, Cheryl Praeger and Jason Semeraro)

## Published academic papers

- 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. - Abelian covers of alternating groups (with Daniel Barrantes and Jeremias Ramirez), to appear in
*Archiv der Mathematik.* - Perfect commuting graphs (with John Britnell), to appear in
*Journal of Group Theory.* - Quasirandom group actions, to appear in
*Forum of Mathematics (Sigma).* - (with Neil Gillespie and Jason Semeraro) Conway groupoids and completely transitive codes, to appear in
*Combinatorica.* - On a conjecture of Degos, to appear in
*Cahiers de topologie et geometrie differentielle categoriques*. - (with Neil Gillespie, Tony Nixon and Jason Semeraro) Generating groups using hypergraphs.
*Quarterly Journal of Mathematics,*(2016) 67 (1), 29-52*.* - Transitive projective planes and insoluble groups.
*Transactions of the American Mathematical Society _368 (2016), 3017-3057*._ - (with Azizollah Azad and John Britnell) Nilpotent covers and non-nilpotent subsets of finite groups of Lie type.
*Forum Mathematicum*27 (2015), 3745-3782. - (with Harald Helfgott and Misha Rudnev). On growth in an abstract plane.
*Proceedings of the American Mathematical Society*143 no. 8 (2015), 3593-3602. - (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. - (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. - Orientably regular maps with Euler characteristic divisible by few primes.
*Journal of the London Mathematical Society*, 88 (2013), no.1, 118–136. - (with Ian Short). Conjugacy in Thompson’s group $F$.
*Proceedings of the American Mathematical Society*, 141 (2013)1529–1538. - (2,m,n)-groups with Euler characteristic equal to $-2^as^b$.
*Electronic Journal of Combinatorics*, 20 (2013), no. 3, R8. - A note on the Weiss conjecture.
*Journal of the Australian Mathematical Society*, 95 (2013), no.3 356-361. - (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. - (with Anupam Singh). Real and strongly real classes in ${\rm SL}
*n(q)$. _Journal of Group Theory*, 14 (2011), no.3, pp. 437–459. - (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. - (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. - (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. - (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. - (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. - Transitive projective planes.
*Advances in Geometry*, 7 (2007), no.4, 475–528. - PSL(3,q) and line-transitive linear spaces.
*Beiträge zur Algebra und Geometrie*, 48 (2007), no.2, 591–620. - Polar spaces and embeddings of classical groups.
*New Zealand Journal of Mathematics*, 36 (2007), 175–184. - Linear spaces with significant characteristic prime. __Innovations in Incidence Geometry, 3 (2006), 109–119.
- Nilpotent Singer groups.
*Electronic Journal of Combinatorics*, 13 (2006), no.1, R94.</ol>

## 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.

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:

- The width of a finite simple group at
*Groups and Geometries 2011*. - Constructing groupoids from designs at
*Groups and Geometries 2015*.