Research

Published and to appear
- Non-free points for groups generated by a pair of 2x2 matrices,
J. Lond. Math. Soc. (2) 62 (2000), 795-801
- A note on torsion groups generated by pairs of 2x2 rational parabolic matrices,
Bull. Aust. Math. Soc. 61 (2000), 151-152,
with Grant Cairns.
- The crystallographic restriction, permutations, and Goldbach's Conjecture,
Amer. Math. Monthly 110 (2003), 202-209,
with Grant Cairns and Devin Kilminster.
- Finite permutation groups with a transitive minimal normal subgroup,
Proc. London Math. Soc.(3) 89 (2004), pp. 71-103,
with Cheryl E. Praeger.
- Symplectic spreads,
Designs, Codes and Cryptography 32 (2004), pp. 9-14
(Special Issue: Proceedings of the Third Pythagorean Conference),
with Simeon Ball, Michel Lavrauw, and Tim Penttila.
- Totally Goldbach numbers and related conjectures,
Austral. Math. Soc. Gaz. 31 (2004), pp. 251-255,
with David van Golstein Brouwers and Grant Cairns.
- Bounds and quotient actions of innately transitive groups,
J. Aust. Math. Soc. 79 (2005), pp. 95-112.

- Transitive eggs,
Innov. Incidence Geom. 4 (2006), pp. 1-12.
with Tim Penttila,
(supported by ARC discovery grant DP0450695).

- Tight sets and m-ovoids of finite polar spaces,
J. Combin. Theory Series A. 114 (2007), no. 7, 1293-1314
with Shane Kelly, Maska Law and Tim Penttila.
(supported by ARC discovery grant DP0450695).

- Transitive decompositions of graph products: rank 3 grid type, J. Group Theory 11 (2008), no. 2, 185-228
with Geoffrey Pearce and Cheryl E. Praeger.
(supported by ARC discovery grant DP0450695).

- A construction of one-dimensional affine flag-transitive linear spaces,
Finite Fields and their Applications 14 (2008), no. 2, 537-548
with Michael Pauley.

- Overgroups of cyclic Sylow subgroups of linear groups,Communications in Algebra 36 (2008), no. 7, 2503-2543
with Tim Penttila.
(supported by ARC discovery grant DP0450695).

- Elation generalised quadrangles for which the number of lines on a point is the successor of a prime,
J. Aust. Math. Soc. 85 (2008), no. 3, 289–303,
with Tim Penttila and Csaba Schneider.
(supported by a Marie Curie IIF (no. MIIF1-CT-2006-040360).

- A hemisystem of a nonclassical generalised quadrangle,
Designs, Codes & Cryptography, 51 (2009), no. 2, 157–165
with Frank De Clerk and Nicola Durante.
(supported by a Marie Curie IIF (no. MIIF1-CT-2006-040360).

- A classification of transitive ovoids, spreads, and m-systems of polar spaces,
Forum Mathematicum, 21 (2009), no. 2, 181–216
with Tim Penttila.
(supported by ARC discovery grant DP0450695).

- Tight sets and m-ovoids of generalised quadrangles, Combinatorica, 29 (2009), no. 1, 1–17
with Maska Law and Tim Penttila
(supported by ARC discovery grant DP0450695).

- Intriguing sets of partial quadrangles,
submitted,
with Frank De Clerck and Nicola Durante.
(submitted December 2008)
(supported by a Marie Curie IIF (no. MIIF1-CT-2006-040360).

- Some characterisations of the Split Cayley hexagon,
submitted,
with Nicola Durante.
(submitted April 1 2009)
(supported by a Marie Curie IIF (no. MIIF1-CT-2006-040360).
In Preparation - Finite 3/2-transitive permutation groups, with Michael Giudici, Martin Liebeck, Cheryl Praeger, and Jan Saxl. - On the association scheme arising from the lines of a polar space, with Frédéric Vanhove.
- Four curious lines of PG(5,3) and a construction of Mathon’s perp-system, with Frank De Clerck
- On the elation group of the dual of the H(4,q2) generalised quadrangle, with Michel Lavrauw and Tim Penttila.

For information on the new hemisystem, please see this page.

My research is mostly in of finite permutation group theory and finite geometry, but I have dabbled a bit in elementary number theory and graph theory. Below is a reasonably up to date list of the papers I have been involved with. If you would like a preprint or more details on a particular paper, feel free to ask me.

Currently, I have an Erdös number of 3 and a Giudici number of 2.