Discrete harmonic analysis, additive number theory/combinatorics and ergodic theory.

One of my main interests are discrete analogues of problems in classical Euclidean harmonic analysis, where the underlying space is the set of lattice points. In this case oscillatory integrals are replaced by exponential sums, and methods of analytic number theory, such as the so-called circle method, become an essential tool.

I have been also interested in problems of additive number theory/combinatorics where one studies arithmetic properties of subsets of positive upper density of integers or integer lattices or possibly other arithmetic sets such as primes or prime tuples.