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Dr William J. Harvey

BillHarveyTelephone: +44 020 7848 2828


Office: K.4U21, King's Building, Strand Campus

Title: Emeritus Reader in Geometry


Bill Harvey received a BSc in Mathematics at Birmingham in 1962 and a PhD from the same institution in 1966. After 3 years at Columbia University in New York and a further 3 years at Polytechnic Institute of Brooklyn, he returned to the UK and has been at King's College London ever since, with the exception of sabbaticals in 1978-79 as a visiting member at IAS in Princeton, 1985-86 as a visitor at IHES, Bures-sur-Yvette and 1996 at CUNY Graduate Center, New York.

He retired from full-time teaching in 2007 and is now Emeritus Reader in Mathematics at King's.

An enthusiastic participant at research conferences, he has contributed over 30 articles to journals and conference publications and has edited one book comprising the Proceedings of an Instructional Conference and two books of research conference articles.

Research Interests

Research Interests include

  • discrete group actions, especially modular groups ;
  • complex analysis and geometry of Riemann surfaces;
  • geometry and topology of low dimensions (<5, say);
  • moduli spaces and their geometry;
  • Kleinian groups and their deformation spaces.

Bill's research is concerned with two main strands of mathematics, discrete group theory and complex analysis, focussing on the space of moduli for compact Riemann surfaces. In addition, there are several aspects of geometry and topology in low dimensions where these theories have great influence, notably in the study of hyperbolic 3-manifolds and Kleinian groups. Riemann surfaces also appear as intrinsic ingredients in much of complex dynamics and in theoretical physics, especially string theory.

Selection of Publications

Recent Publications

Homomorphisms from mapping class groups (with M. Korkmaz) Bull. London Math. Soc. 37 (2005), 275-284.

Thompson's group as a Teichmuller mapping class group (with E. de Faria & F.P. Gardiner) in In the Tradition of Ahlfors & Bers III , Contemp. Math. 355 (2004), 165- 185.

Remarks on the curve complex: classification of surface homeomorphisms LMS L. Note Series 299 (2003), 165-179.

On families of algebraic curves with symmetry (with G. Gonzalez-Diez) in Complex Manifolds & Hyperbolic Geometry, Contemp. Math. 311 (2002), 261-276. [PS]

Universal Teichmuller Space (with F. P. Gardiner) Chapter 14 in Handbook of Complex Analysis (ed. R. Kuhnau), Elsevier Press, 2002. [PS]

Mating quadratic maps with Kleinian groups (with S.R. Bullett) AMS Electronic Res. Ann. 6 (2000), 21-30.


Current Preprints

Teichmuller spaces, triangle groups and Grothendieck dessins (to appear in Europ.Math. series, 2006).

Surface topology: Macbeath, Grothendieck and Thurston (in preparation)

List of Published Articles (from 1966 to 2006)

HRI Lectures on the mapping class group June 2005

HRI Lectures on the mapping class group.


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