My research is in Random Matrix Theory - in particular looking at the eigenvalue statistics and properties of characteristic polynomials of various random matrix ensembles.  

For many years I have considered the connection between Random Matrix Theory and certain number theoretical functions such as the Riemann zeta function and L-functions. This connection arises through the statistics of the zeros of these functions and can be exploited, allowing us to study zeta and L-functions using the well-developed techniques of Random Matrix Theory.

Now I am developing an interest in using random matrix theory in biology - to investigate the statistical distribution of events on chromosomes.  

PHD PROJECTS: I'm happy to supervise PhD projects in random matrix theory.  The mathematics can be very varied, with previous projects including techniques from probability, analysis, manipulating matrix determinants, combinatorics and computation.  We can also discuss applications to biology.