# Research

I have interests in several research topics, mainly focused on groups and their representations. In this section of the website, you can find out more about my research, which are listed in no prticular order, and download preprints of my research.

Publications: a list of publications, preprints, and articles in the process of being written. This includes copies of the papers where available, and my theses.

Algebraic Modules: my D.Phil. thesis was on modular representation theory, and in particular, the study of algebraic modules.

Combinatorics: I work on combinatorics associated with the symmetric group and the partition function.

Infinite Group Theory: I have a deep interest in group theory, both finite and infinite. In joint work with George Wellen, who did his D.Phil. at the University of Oxford, I studied the groups generated by (2,3)-automata.

Representation Growth: following on from my work in symmetric group representation theory, I have studied representation growth of infinite, finitely generated groups.

The Unit Conjecture: joint with Peter Pappas of Vasser College, NY, I have studied the well-known Unit Conjecture, which asks what the group of units of a group ring of a torsion-free group are. It is conjectured that all units are multiples of group elements.

Chemistry: combining pure and applied mathematics with straight chemistry, Gregory Wildgoose of the chemistry department and I have worked on problems associated with carbon nanotubes.

Fusion Systems: I gave a lecture course on the emerging theory of fusion systems, which attempts to combine local finite group theory with representation theory. As a consequence of giving the course, I started doing research in the area.