My research is currently focussed on dependent type theory.
Dependent type theory (à la Marin-Löf) seeks to be a foundation for formal reasoning in mathematics and computer science. Its powerful concept of introduction, elimination and computation rules has proven a robust and extensible way of organising formal reasoning. Homotopy type theory (initiated by the late Vladimir Voevodsky) is a recently developed flavour of dependent type theory – where higher dimensional mathematical objects reside as first-class objects.
My contributions to the field includes a model of multisets and a simplification of the model of set theory in homotopy type theory. Further more, I have contributed to the theory of containers, a model of data structures in type theory, by extending the notion to data structures with symmetries.