About Me

 
 

My research has been in Fuchsian group and Non-Euclidean crystallographic (NEC) groups and their applications to Riemann surfaces and dessins d'enfants. My first work was on the structures of the groups themselves. I then applied NEC groups to study symmetries of Riemann surfaces and the topology of real algebraic curves. This has led to a long-standing collaboration with mathematicians from Spain. The initial work I did in Southampton on Maps and Hypermaps, often with Gareth Jones and many research students, turned out to be an early version of the theory of dessins d'enfants, which is now a significant research topic in Mathematics linking together many areas such as Galois theory, group theory, graph theory, algebraic curves, moduli spaces and Belyi Theory.

Research Interest

Postal Address

School of Mathematics

University of Southampton

Southampton

SO17 1BJ

United Kingdom

e-mail: ds@maths.soton.ac.uk

Office telephone: 02380-595157

Research Students

  1. 1.Wendy Hall: Automorphisms and coverings of Klein surfaces (1978)

  2. 2.Robert Riley: Projective representations of link groups (1980)*

  3. 3.Robin Bryant: Maps on surfaces with boundary (1984)

  4. 4.Stephen Harding: Some algebraic and geometric problems concerning discrete groups (1985)

  5. 5.David Corn: Regular Hypermaps (1989)

  6. 6.Mehmet Akbas: The normalizer of Modular subgroups (1989)

  7. 7.Derek Jennings: An investigation into modular forms, q-series, partitions and related topics (1992)*

  8. 8.Ismail Cangul: Normal subgroups of Hecke groups (1993)

  9. 9.Paul Watson: Symmetries and automorphisms of compact Riemann surfaces (1995)

  10. 10.Robert Syddall: Uniform dessins of low genus (1997)

  11. 11.Adnan Melekoglu: Symmetries of Riemann surfaces and regular maps (1998)

  12. 12.Ioannis Ivrissimtzis: Congruence subgroups of Hecke groups and regular dessins (1998)

  13. 13.Catherine Kelk: Four-punctured spheres (1999)

  14. 14.Catherine Campbell-Grant: Hecke groups and their subgroups of low index (2008, MPhil)

  15. 15.Zoë Laing: Transitivity of Weierstraß Points on Riemann Surfaces (2008)

(The * refers to students who chose their own topic and mainly worked independently.)

Other Interests

Liberal Politics.  My wife Margaret has been a Councillor in Southampton for 15 years, and from 1995-96 was the first Liberal Democrat Mayor in the city. For several years we have campaigned together in Southampton and elsewhere.

Music.  My other main interest is in (mainly) classical music.  I have taken a particular interest in the music of the great Austrian composer Anton Bruckner.