Richard Borcherds
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| Richard Borcherds | |
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| Born | November 29, 1959 Cape Town, South Africa |
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| Residence | U.K., U.S. |
| Nationality | British[1] |
| Fields | Mathematician |
| Institutions | University of California, Berkeley, University of Cambridge |
| Alma mater | University of Cambridge |
| Doctoral advisor | John Horton Conway |
| Known for | Lattices, number theory, group theory |
| Notable awards | Fields Medal (1998) |
Richard Ewen Borcherds (born November 29, 1959) is a British mathematician specializing in lattices, number theory, group theory, and infinite-dimensional algebras. He was awarded the Fields Medal in 1998.
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[edit] Personal life
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 alternating positions at Cambridge and the University of California, Berkeley. He is currently Professor of mathematics at Berkeley, having previously held a Royal Society Research Professorship in Cambridge.
In his teens Borcherds was a promising chess player.[2] An interview with Simon Singh for the Guardian, in which Borcherds suggested he might have some symptoms of Asperger's syndrome,[3] subsequently led to a chapter in a book by Simon Baron-Cohen.[4][5]
He was Midlands under 21 Chess Champion at age 14.
[edit] Work
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 monstrous moonshine conjecture by Conway and Norton, relating the monster group 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. In recent years, Borcherds has been attempting to construct quantum field theory in a mathematically rigorous manner.
[edit] Awards
In 1992 he was one of the first recipients of the EMS prizes awarded at the first European Congress of Mathematics in Paris. 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."
[edit] References
- ^ Goddard, Peter (1998), The work of Richard Ewen Borcherds, "Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998)", Documenta Mathematica: 99–108, arΧiv:math/9808136, ISSN 1431-0635, http://www.emis.de/journals/DMJDMV/xvol-icm/Laudationes/13goddard.MAN.html.
- ^ Baron-Cohen, Simon. "A Professor of Mathematics". 161. http://leitl.org/docs/a-professor-of-mathematics.pdf. Retrieved on 2009-01-18.
- ^ Simon Singh, "Interview with Richard Borcherds", The Guardian (28 August 1998)
- ^ Baron-Cohen, Simon (2004), The Essential Difference: Male and Female Brains and the Truth about Autism, Basic Books, ISBN 0-465-00556-X. Chapter 11, "A Professor of Mathematics" (see external links) records conversations with Richard Borcherds and his family.
- ^ High flying obsessives, The Guardian, December 2000
[edit] Sources
- 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.
[edit] 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).
- Richard Borcherds' web site (has links to some relatively informal lecture notes describing his work)
- BBC News (1998): British academics win top maths awards
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