My interest is in finite and infinite groups and its actions.
Groups and geometries
For instance structure of finite groups; Kac-Moody Groups; Aut(F_n); reflection
groups, Coxeter groups and generalisations (such as elliptic Weyl groups).
Presentation of groups and the underlying combinatorics
For instance Artin groups; in particular the dual
approach to Coxeter and Artin groups as well as to elliptic Weyl groups; Hurwitz action; non-crossing partition
posets and lattices.
This is the latest research topic
Permutation groups acting on finite or infinite sets
For instance regular subgroups of primitve permtutaion
Group theory and applications
For instance permutation polytopes; Cryptography