I use methods from homological algebra and K-theory to study groups and their integral representations. I am particularly interested in arithmetic groups, mapping class groups, and their (rational) Euler characteristics.

I am interested in the ideas of approximation, cotorsion pairs, and singularity categories as introduced by Auslander and Buchweitz. In particular, applying the generalised theory of Gorenstein projective approximations to non-commutative integral group rings.

Much more broadly, most problems that involve the action of an (infinite, discrete) group on some space or object I find interesting. To name a few examples; groups acting on trees and Bass-Serre Theory, lattices in semisimple Lie groups and their relation to arithmetic groups, the topology and combinatorics of group presentations and the associated 2-dimensional cell complexes.