# Research

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

## Submitted papers

- Large minimal invariable generating sets in the finite symmetric groups (with Daniele Garzoni)
- On the number of conjugacy classes of a primitive permutation group with nonabelian socle (with Daniele Garzoni)
- Nilpotent covers of symmetric groups (with Kimeu Arphaxad Ngwava and Ian Short)
- Groups obtained from 2-(n,4,L) designs (with Jeremias Ramirez)
- A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank (with Laszlo Pyber and Endre Szabo)

## Published academic papers

- Nilpotent covers of dihedral groups (with Kimeu Arphaxad Ngwava) to appear in
*Ars Combinatoria*. - The character table of a sharply 5-transitive subgroup of the alternating group on 12 letters (with Sam Hughes) to appear in
*International Journal of Group Theory*. - Binary groups: Alternating and classical groups (with Pablo Spiga),
*Amer. J. Math.*142, No. 1, 1-43 (2020). - 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). - 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). - 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). - Cherlin’s conjecture for sporadic simple groups (with Francesca Dalla Volta and Pablo Spiga),
*Pac. J. Math.*297, No. 1, 47-66 (2018). - Conway groupoids and completely transitive codes (with Neil Gillespie and Jason Semeraro),
*Combinatorica*38, No. 2, 399-442 (2018). - Perfect commuting graphs (with John Britnell),
*J. Group Theory*20, No. 1, 71-102 (2017). - Quasirandom group actions,
*Forum of Mathematics (Sigma)*4, Article ID e24, 35 p. (2016). - Abelian covers of alternating groups (with Daniel Barrantes and Jeremias Ramirez),
*Archiv der Mathematik.*107, No. 2, 135-150 (2016). - On a conjecture of Degos,
*Cah. Topol. Géom. Différ. Catég.*57, No. 3, 229-237 (2016). - Generating groups using hypergraphs (with Neil Gillespie, Tony Nixon and Jason Semeraro),
*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. - Nilpotent covers and non-nilpotent subsets of finite groups of Lie type (with Azizollah Azad and John Britnell).
*Forum Mathematicum*27 (2015), 3745-3782. - On growth in an abstract plane (with Harald Helfgott and Misha Rudnev),
*Proceedings of the American Mathematical Society*143 no. 8 (2015), 3593-3602. - Growth in solvable subgroups of GL_r(Z/pZ) (with Harald Helfgott),
*Mathematische Annalen*360 (2014), no. 1-2, 157-208. - 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. - Orientably regular maps with Euler characteristic divisible by few primes.
*Journal of the London Mathematical Society*, 88 (2013), no.1, 118–136. - Conjugacy in Thompson’s group F (with Ian Short),
*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. - 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. - Real and strongly real classes in SL(n,q) (with Anupam Singh),
*Journal of Group Theory*, 14 (2011), no.3, pp. 437–459. - 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. - Growth of small generating sets in SL(n,pZ/Z) (with Harald Helfgott),
*International Mathematics Research Notices*, 18 (2011), 4226–4251. - 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. - 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. - 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. - 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.

## 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*.