- Departmental Research Fellow in the Mathematical Institute, Oxford.
- Fellow of Christ's College, Cambridge.
- Honorary Professor of the University of Leipzig.

From 2004 to 2010 I was Professor of Mathematics, Oxford University and also taught undergraduates at University College, Oxford, latterly as Distinguished Research Lecturer.

I held the Mason Chair of Mathematics at the University of Birmingham from 1994 to 2003 and an Honorary Visiting Professorship at Aston University from 2005 to 2014. I have held visiting professorships for various periods at 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, May--June, 2009), Berlin (September 2011). From October 2014 -- March 2015 I was the Leibniz Professor at the University of Leipzig.

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*.

There is a blog about this last result.

I have been the Editor-in-Chief of this journal from its foundation until December 2017. High quality manuscripts can be submitted to me (at jgt@maths.ox.ac.uk) or any other member of the Editorial Board. Before submitting, please consult the Notes for Authors. Enquiries about subscriptions should be addressed to the publishers, W de Gruyter.

Music is an important part of my life, especially the music of J. S. Bach and some of his predecessors, W. A. Mozart, B. Britten and some other 20th century composers. (For connections between music and mathematics, see The Glass Bead Game.) I sing with various choirs, most recently the Oxford Bach Choir and the Zürcher Bach Chor, the Leipziger Bach Chor and the Christ Church Cathedral Singers. I am interested in modern languages: I am interested in modern languages and I have lectured frequently in German and Italian, most recently to students in Leipzig.