Research interests:
* Algebra, Geometry, Topology and Number Theory:
In particular, Cohomology of arithmetic groups, Modular forms, Equivariant K-homology, Chen/Ruan orbifold cohomology, Algebraic K-theory, but also many other topics.
* Topological Data analysis:
Please see my topological data analysis software HomologyLive
and my related preprint.
A description of my research projects is given in this document (version française ici).
The above animated picture shows, in the hyperbolic view of geomview, 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 -427 to the rational numbers. The picture has been created by my Master student Kelly Jost from data computed with my program Bianchi.gp.
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 Bianchi.gp.