*L*-functions, and have studied intensively various exponential sums related to cusp forms.

I am also very interested in spectral theory in contexts such as analytic number theory, inverse spectral and scattering theory and arithmetic quantum chaos. In particular, I have studied non-scattering energies, transmission eigenvalues and shape identification.

Besides research, the Finnish mathematical olympiad training has a special place in my heart. Though I have been involved in many different aspects of the related activities, I contribute primarily by teaching problem solving and more advanced mathematics, both in a class room and through correspondence, to secondary school and high school students.