My main research field is geometric group theory. I am mainly interested in various aspects of group actions on CAT(0) spaces.
- CAT(0) cube complexes: higher dimensional analogues of trees, higher dimensional splittings.
- Dynamics on CAT(0) spaces: properties of groups acting on CAT(0) spaces, invariant random subgroups of groups acting on CAT(0) spaces.
- Regular CAT(0) complexes: uniqueness of regular CAT(0) cube complexes and polygonal complexes. Properties of highly-symmetric regular complexes
On hyperbolic groups:
- Surface subgroups: Finding and understanding surface subgroups of hyperbolic groups.
- Boundaries: Finding and characterizing new boundaries of hyperbolic groups.