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:
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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.
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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.