My research focuses on the study of groups, but I am also interested in how these fit into the broader setting of algebra and in situations where topological structure arises. My main interest is in structural aspects of groups, both finite and infinite, using a variety of tools to analyze this structure.

Some examples of some of the themes arising within my work include the following topics. By their nature, ideas occurring within one setting has influence on the others.

• Asymptotic properties of families of finite groups, including probabilistic problems (e.g., probabilistic generation).
• Structure of infinite groups with finiteness properties or prescribed properties (e.g., infinite groups with all quotients having specified properties).
• Profinite groups: these are topological groups that arise as the inverse limit of a family of finite groups.
• Totally disconnected locally compact groups.
• Groups acting via homeomorphisms of Cantor space (e.g., Thompson's groups).