- Splittings of groups and group actions on trees. Ends of groups.
- Groups with Eilenberg–Mac Lane spaces of finite type, their structure and their classifying spaces for proper actions.
- Modular Invariant Theory.
- Profinite groups and Galois Cohomology.
- The application of Clausen–Scholze Condensed Maths to the study of Galois Cohomology.