# Biography of Richard Ewen BORCHERDS

South Africa > Science : **Richard Ewen BORCHERDS**

Born on 29/11/1959

*(format : day/month/year)***Biography :****Richards Ewen Borcherds** born November 29, 1959, is a British mathematician of of South african origin. specializing in lattices, number theory, group theory, and infinite-dimensional algebras.

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."

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.

In his teens Borcherds was ranked as one of the most promising chess players in the UK.He was diagnosed with Asperger syndrome by Simon Baron-Cohen.

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 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.

Borcherds began his academiccareer at Trinity College, Cambridge before going as assistant professor tothe University of California in Berkeley. He has been made a Fellow of theRoyal Society, and has also held a professorship at Berkeley since 1993.

*Last update : 08/20/2010*

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