Richard Borcherds
Richard Borcherds | |
|---|---|
| Born | November 29, 1959 |
| Nationality | English  |
| Alma mater | University of Cambridge |
| Known for | Lattices, number theory, group theory |
| Awards | Fields Medal (1998) |
| Scientific career | |
| Fields | Mathematician |
| Institutions | University of California, Berkeley, University of Cambridge |
| Doctoral advisor | John Horton Conway |
| Doctoral students | Daniel Allcock, Alexander Barnard, Tathagata Basak, Oliver King, Peter Niemann, Sankaran Viswanath |
Richard Ewen Borcherds (born November 29, 1959) is a British mathematician specializing in lattices, number theory, group theory, and infinite-dimensional algebras.
He was born in Cape Town and educated at King Edward's School, Birmingham and Cambridge University, where he studied under John Horton Conway. After receiving his doctorate he has held various positions at Cambridge and at the University of California, Berkeley, where he is currently a professor of mathematics.
Borcherds is best known for his work connecting the theory of finite groups with other areas in mathematics. In particular he invented the notion of vertex algebras, which Igor Frenkel, James Lepowsky and Arne Meurman used to construct an infinite-dimensional graded algebra acted on by the monster group. Borcherds then used this, and methods from string theory, to prove the Conway-Norton conjecture, relating the monster to the coefficients of the q-expansion of the j invariant. The result was not only a great increase in understanding of the monster group, a very large finite simple group whose structure was previously not well-understood, but tied the monster to various aspects of mathematics and mathematical physics. (See monstrous moonshine.) In recent years, Borcherds has been attempting to construct quantum field theory in a mathematically rigorous manner.
In 1998 at the 23rd International Congress of Mathematicians in Berlin, Germany he received the Fields Medal together with Maxim Kontsevich, William Timothy Gowers and Curtis T. McMullen. The award cited him "for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and Borcherds' Lie algebras, the proof of the Conway-Norton moonshine conjecture and the discovery of a new class of automorphic infinite products."
In his teens Borcherds was ranked as one of the most promising chess players in the UK.
External links
- "Borcherds, Gowers, Kontsevich, and McMullen Receive Fields Medals", Notices of the American Mathematical Society, Volume 45, Number 10 (November 1998).
- James Lepowsky, "The Work of Richard Borcherds", Notices of the American Mathematical Society, Volume 46, Number 1 (January 1999).
- Richard Borcherds, "What is ... The Monster?", Notices of the American Mathematical Society, Volume 49, Number 9 (October 2002).
- Simon Singh, "Interview with Richard Borcherds", The Guardian (28 August 1998).
- Richard Borcherds' web site (has links to some relatively informal lecture notes describing his work)
- BBC News (1998): British academics win top maths awards
References
- Conway and Sloane, Sphere Packings, Lattices, and Groups, Third Edition, Springer, 1998 ISBN 0-387-98585-9.
- Frenkel, Lepowsky and Meurman, Vertex Operator Algebras and the Monster, Academic Press, 1988 ISBN 0-12-267065-5.
- Kac, Victor, Vertex Algebras for Beginners, Second Edition, AMS 1997 ISBN 0-8218-0643-2.
