STEM Faculty

Professional biography

I joined the OU in October 2021 as a Lecturer in Pure Mathematics. Prior to that I held academic positions at the University of South Wales, the University of Costa Rica, the University of Bristol and the Institute for Mathematical Sciences in Chennai, India. 

I work at the OU 2 days a week; for the remainder of the week I am a Project Manager at the Sortition Foundation. More information is available at my personal website.

Research interests

I am interested in group theory which is an area of algebra concerned with the mathematical study of symmetry. Some particular interests are:

1. Relational complexity: This is a statistic associated with finite permutation groups and originating in model theory. I have spent a lot of time trying to understand when finite permutation groups have relational complexity as large as possible or as small as possible. For the latter situation there is a famous conjecture of Cherlin which describes those primitive groups with RC=2. Martin Liebeck, Pablo Spiga and I held an EPSRC grant aimed at proving this conjecture: we were successful! A full account of the proof of the conjecture has now been published. In April 2025, Martin, Pablo and I, together with Pierre Guillot, embarked on new work, also funded by the EPSRC, to push this work further.
2. Growth in groups: The study of how sets grow inside groups turns out to have applications in all sorts of areas of mathematics, from number theory to graph theory. I worked with Harald Helfgott to prove a particular case of the Helfgott-Lindenstrauss conjecture. This conjecture gives conditions under which subsets of finite linear groups grow rapidly. I also held an EPSRC grant to work on a related conjecture due to Liebeck, Nikolov and Shalev. This conjecture has now been proved in joint work with Lifshitz, Pyber and Szabo.
3. Groups and finite geometry: Finite groups are connected to finite geometries in many ways: most obviously they can occur as automorphism groups and I have studied this situation in the case where the geometry in question is a finite projective plane. I have also studied how finite geometries can be used to "generate" groups and, with Neil Gillespie and Jason Semeraro, discovered some new ways to generate certain finite simple groups.