University of Durham --- Department of Mathematical Sciences

Professor John R. Parker

Department of Mathematical Sciences
Durham University
Science Laboratories
South Road
Durham, DH1 3LE
United Kingdom

0191 334 3057
Department fax:
0191 334 3051
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Hyperbolic geometry

I work in this general area. Our department logo at the top right hand corner of this page depicts the Poincaré disc model of the hyperbolic plane together with the fundamental domain for an ideal triangle group and several of its images. It may be found on the floor of the entrance to the department. The group is generated by reflection across the sides of the triangle. This group is rigid in the sense that any two such groups are conjugate via a Möbius transformation. On the other hand if we ask an analogous question for complex hyperbolic space there is a one parameter family of inequivalent groups, see the paper (with Bill Goldman) in J. reine angewandte Math in my publications list.

At the moment I mostly work on :

Complex hyperbolic geometry Many of the questions that can be asked for discrete groups of (real) hyperbolic isometries can be asked for complex hyperbolic isometries. However the answers can often be surprising and usually involve rather different methods. This means that complex hyperbolic geometry is a rather exciting field to work in.

Geometriae Dedicata

Between January 2013 and December 2022 Jean-Marc Schlenker and I were joint Editors-in-Chief of Geometriae Dedicata. From January 2023 Richard Wentworth has taken over from us as Editor-in-Chief. We would welcome the the submission of good papers in the area of geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas.



Note: The papers listed here are not all linked to retrievable files. And those that are are not necessarily the final versions and so they should be treated as "for information only".

Book Reviews