Research interests: Algebra, Geometry, Topology and Number Theory; for instance:

- Cohomology of arithmetic groups,

- Modular forms,

- Equivariant K-homology,

- Chen/Ruan orbifold cohomology,

- Algebraic K-theory,

- and many others.

A detailed description of my current research projects is given here.

This picture shows, in the upper-half space model, the non-vertical part of the boundary of a fundamental domain in hyperbolic three-space for the Bianchi Group SL(2, A), with A the ring of integers in the imaginary quadratic number field obtained by adjoining the squareroot of -37 to the rational numbers. The picture has been created by my co-author Mathias Fuchs from data computed with my program

I have organised (jointly with Sejong Park) the conferences "Groups in Galway 2014" and "Groups in Galway 2015".

In 2016, I have organised the Bianchi Modularity Workshop, in Luxembourg.

In 2017, I have organised the Colloquium on the Geometry of Groups and Numbers at Université Pierre et Marie Curie, Institut Mathématique de Jussieu - Paris Rive Gauche.

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