# Research interests

My research focuses on the algebraic objects known
as *groups*. These arise throughout mathematics as the
set of symmetries of other mathematical structure. I am
interested in both finite and infinite groups and their
structure. I am also interested in ways that group
theoretical properties apply to wider classes of algebraic
structure.

Specific examples of my research interests include:

- generation sets for groups and other algebraic structures;
- probabilistic generation of finite and profinite groups;
- links between the algebraic structure and the topological structure of profinite groups;
- groups arising from transformations of a variety of combinatorial structures (e.g., Thompson's groups, automorphisms of Fraïssé limits, etc.);
- groups identities and properties of varieties of groups.