I'm generally interested in any topic of analytic number theory, and the problems I'm currently working on involve:
Primes: I'm looking at ``Barban-Davenport-Halberstam" moments of primes, with the aim of providing evidence that the primes obey a Gaussian law in short intervals, as in the conjectures of Montgomery and Sound. Recently I confirmed that the third moment follows this law, substantially improving on a result of Hooley.
Divisor functions: I'm looking at divisor functions in arithmetic progressions, the motivation being the links with gaps between primes. Sometimes some arithmetic gets untangled when averaging, for example an application of Voronoi's formula shows d_4(n) to have exponent of distribution quite a bit >1/2 when taking an average over a in arithmetic progressions. I'm also interested in the problem of averaging over q, in fact variances of arithmetic sequences in general interest me and I've obtained, for example, a theorem of Montgomery-Hooley type for higher d_k(n).
L^1 means of exponential sums: I've shown that the circle method in its classical form can give bounds for L^1 means of exponential sums of arithmetic functions - in particular for divisor functions.