- Property (T) and its many generalizations and implications
- High dimensional expanders and their applications to theoretical computer science
- Coarse geometry and especially aspects of dimension such asymptotic dimension and property A
- Geometric group theory
This list of research interests is not comprehensive and pursuing questions regarding these interests often lead my to use (or develop) tools from other areas of mathematics such as algebraic topology, functional analysis, geometry of Banach spaces, graph theory, representation theory and more.