Teaching & Administration.

• elected member of the UWS Academic Senate and the School Academic Standards and Quality Committee,
• member of the School Research Committee.

Research.

My main research interests are within algebra.  More narrowly the questions I attempt to answer lie within the representation theory of finite groups.  Finite groups are ubiquitous in many parts of mathematics and sciences more broadly, and questions about their structure can often be accessed by considering how they can be "represented" within groups of matrices.  This question in turn led historically to the study of Iwahori-Hecke algebras, which are deformations, or "q-analogues", of the group algebras of finite reflection groups. 

My research has focussed on questions about the structure of Iwahori-Hecke algebras of both the real reflection groups (Coxeter groups) and the Hecke algebras of finite complex reflection groups.  Specifically most questions I have looked at relate to the structure of the centres of these algebras (that part which commutes with all other elements in the algebra).

I also work on applied scientific questions.  In particular I have been working on the question of how to best understand the immensely detailed genetic data arising from an outbreak of infectious disease such as tuberculosis.   I am interested in how mathematics can help describe the processes underlying the science we observe.  This work has been with Dr Mark Tanaka at UNSW, and has been funded by ARC Discovery Grants (2005-2007 and 2009-2013). 

Students interested in studying any of these areas should contact me or consult my list of specific student projects.

Other sites of interest:

Contact details: