My research is focused on the study of the Riemann zeta function along the critical line. One approach to this problem stems from Random Matrix Theory, as the eigenvalues of Random Unitary (or Hermitian) matrices are a good model for the zeros of zeta (Dyson-Montgomery c.1980).
By studying matrices in the Circular Unitary Ensemble (Unitary matrices with Haar measure) the goal is to better understand the growth of the zeta function along the critical line. This approach utilises tools from analysis, number theory and probability theory (invoking methods from Farmer, Gonek, Hughes, one can model zeta as a partial product over zeros times a partial product over primes; we model the product over zeros via RMT, while the other term can be modelled via Large Deviations theory).
More generally, my research interests lie in Analytic Number Theory, however I am also interested in other aspects and applications of Number Theory such as Elliptic Curves and Cryptography.