My research is in the area of geometric group theory. In particular, I am interested in various notions of negative curvature in group theory and how these relate to the algebra, geometry, analysis, and logic of groups. Most of my work has focused on the classes of hyperbolic, relatively hyperbolic and acylindrically hyperbolic groups. Some specific topics which I have thought or written about include:

Generalizations of small cancellation theory
Conjugacy growth functions
Quasi-cocycles, bounded cohomology and stable commutator length
Asymptotic cones
Transitivity degrees and highly transitive actions
The elementary/universal theory of groups and equations in groups
Limit groups and Makanin-Razborov diagrams
Descriptive set theory and the space of marked groups

My papers can be found on the arXiv