JOHN S. WILSON, M.A., Sc.D. (Cantab.), L.R.A.M.

Positions held

Professor of Mathematics, University of Oxford and Distinguished Research Lecturer, University College, Oxford.

For the past three years I have been responsible for the 16 lectures of the fourth year Oxford Lie algebras course. I also give classes and tutorials in various subjects to undergraduates at University College.

I remain a Fellow of Christ's College, Cambridge, where I taught for 25 years, and I return from time to time for spells of uninterrupted work and to see many long-standing friends. From 1994 to 2003 I held the Mason Chair of Mathematics at the University of Birmingham. I hold an Honorary Visiting Professorship at Aston University. I have been visiting professor for various periods at a number of other universities around the globe, most recently the Université de Genève (January-June, 2002), the University of California at San Diego (January-March, 2004), ETH Zürich (April-June, 2007).

Research interests

profinite groups, finite and infinite soluble groups, model theory of groups, branch groups, word growth of groups, finitely presented groups, generation problems for finite simple groups.

I particularly like results with simple uncluttered statements. (Of course many important results cannot take this form.) I have proved, for example, that

if G is a group having a presentation with n generators and r relators, and S is any finite subset that generates G, then there are n-r elements of S that freely generate a free subgroup.
(with R. M. Guralnick) a finite group G is soluble if with probability > 11/30 two randomly chosen elements generate a soluble subgroup.
(with R. I. Grigorchuk) any two infinite finitely generated subgroups of the Grigorchuk group have isomorphic subgroups of finite index.
a finite group is soluble if and only if no non-trivial element g is a product of 56 commutators of pairs of conjugates of g.

Extra-curricular activities

Music is an important part of my life, especially the music of J. S. Bach and some of his predecessors, and of some 20th century composers. (For connections between music and mathematics, see The Glass Bead Game.) So, too, are my wife Natasha, and my children. I am interested in modern languages: I have lectured frequently in German and Italian, and two ambitions are to give a lecture in French, and to catch up in Russian with my ten-year-old daughter Fiona.