I work on finite groups and compact topological groups, recently exploring possible applications to pseudofinite groups.
- Emeritus Fellow, All Souls College (from 2015)
- Senior Research Fellow, All Souls College and Professor of Mathematics, University of Oxford (from 1991 to 2015)
- Research Fellow, All Souls College (from 1984 to 1991)
- Research Lecturer then Reader in Mathematics, University of Manchester Institute of Science and Technology (from 1979 to 1984)
- Wissenschaftlicher Assistant, University of Bielefeld (from 1976 to 1978)
- Lecturer, Queen Mary College, London (from 1975 to 1976)
- 1851 Research Fellow, Queen Mary College, London (from 1972 to 1974)
- Postgraduate, Queen Mary College, London (from 1969 to 1972)
- Undergraduate, Peterhouse, Cambridge (from 1966 to 1969)
- Algebra: infinite groups, profinite groups, polycyclic groups, Diophantine decision problems, related topics in number theory, commutative algebra, Lie algebras