At the moment, my main interest is in the area of Algebraic Number Theory called Arithmetic Statistics, in particular in the Cohen-Lenstra heuristics on ideal class groups and its many generalisations and variants. I also think about the arithmetic of elliptic curves over number fields, and about the Galois module structure of arithmetic objects, such as rings of integers of number fields, their units, and their higher K-groups. In Representation Theory I think about rational and integral representations of finite groups. I particularly enjoy exploiting connections between representation theory and number theory. Recently, I have also done some research on group actions on the cohomology of low-dimensional manifolds.