My main research area are geometric and arithmetic questions in henselian valued fields, which I consider using model theoretic methods. Typical examples of henselian valued fields are the p-adic numbers and the field of formal Laurent series with coefficients in some other field. More precisely, I am mainly working on the following two topics:
Singularities and stratifications: I proved the existence of a strong notion of stratifications in henselian valued fields. These stratifications in particular induce classical Whitney stratifications over the reals and the complex numbers.
Motivic integration and its applications to representation theory of reductive groups over local fields: Motivic integration makes it possible to compute integrals uniformly in all local fields; this can be applied to make representation theory of reductive groups over local fields uniform in the field.