My current research is in the area Topological Quantum Field Theory in the categorical setting, which means an interest for cobordism categories, infinity categories, module categories, etc. A (short) research statement can be found here.
My past research includes, generalized differential cohomology theories, T-duality, twisted K-theory, gerbes. For a very recent survey on differential cohomology theories, see here.
In my Ph.D. thesis I studied applications of K-theory, K-homology, and KK-theory to theoretical physics, in particular to D-branes and String theory. Moreover, I've built a model for equivariant differential K-theory for a finite group G, which suitably reduces to the Hopkins-Singer model for differential K-theory, and I've investigated the applications of such a construction to the theory of Ramond-Ramond fields in String theory.
Recent coworkers: Christoph Schweigert Jürgen Fuchs Domenico Fiorenza Coworkers and colleagues at Goettingen University: Dorothea Bahns Ralf Meyer Thomas Schick Alexander Kahle Others: Richard Szabo Ulrich Bunke