Richard Borcherds

Richard Borcherds (1993)

Richard Ewen Borcherds (born November 29, 1959 in Cape Town , South Africa ) is a British - American mathematician who works in the areas of group theory , number theory and geometry , especially lattices and infinite-dimensional algebras ( Kac-Moody algebras , vertex algebras ).

Live and act

He grew up in Birmingham, won a gold medal at the International Mathematical Olympiad in 1978 , studied at Cambridge with John Horton Conway (doctorate in 1985 on the Leech grid) and later went to the University of Berkeley in California . In his youth he was one of the leading chess players in England, but then turned entirely to mathematics.

Together with Igor Frenkel , James Lepowsky and Arne Meurman, he developed the theory of vertex algebras , special infinite-dimensional graduated algebras that are used, for example, in string theory . In particular, he found a vertex algebra on which the largest finite simple sporadic group, the monster group , operates and was able to use the moonshine conjectures of John McKay , John Horton Conway and Simon Norton about the appearance of the degrees of the irreducible representations of the monster in the Prove Fourier coefficients of the elliptic module function ( function ). ${\displaystyle j}$

Later he dealt among other things with the mathematical foundations of quantum field theory .

He received the Fields Medal in 1998 at the ICM in Berlin for his work to prove the “monstrous moonshine” properties . In 1992 he received the EMS Prize . He is a Fellow of the American Mathematical Society and the American Academy of Arts and Sciences . In 2014 he was elected to the National Academy of Sciences .

Borcherds told the Guardian newspaper that he had Asperger's Syndrome . The British psychologist Simon Baron-Cohen made the diagnosis after thorough examinations and reported about it in the chapter "A mathematics professor" of his book From the first day differently .

literature

• JH Conway, NJA Sloane: Sphere Packings, Lattices, and Groups. 3. Edition. Springer-Verlag, 1998, ISBN 0-387-98585-9 .
• Igor B Frenkel, J Lepowsky, Arne Meurman: Vertex Operator Algebras and the Monster. Academic Press, 1988, ISBN 0-12-267065-5 .
• Victor Kac: Vertex Algebras for Beginners. 2nd Edition. AMS 1997, ISBN 0-8218-0643-2 .

Web links

• John J. O'Connor, Edmund F. Robertson :  Richard Borcherds. In: MacTutor History of Mathematics archive .
• Fields Medal for Borcherds, Gowers, Kontsevich and McMullen, Notices of the American Mathematical Society, October 1998, English (PDF; 127 kB)
• Lepowsky on "The Work of Richard Borcherds" (PDF; 320 kB) Notices AMS, January 1999 (English)
• Borcherd's "What is ... The Monster?" (PDF; 53 kB) Notices of the AMS, October 2002 (English)
• Simon Singh: "Interview with Richard Borcherds" . The Guardian , August 28, 1998
• Borcherds website with links to his work , his work is also right here
• RE Borcherds, A. Barnard: Lectures on Quantum Field Theory . 2002, arxiv : math-ph / 0204014
• Laudation Fields Medal by Peter Goddard, ICM 1998 Berlin, English
• Literature by and about Richard Borcherds in the WorldCat bibliographic database

Individual evidence

1. ^ National Academy of Sciences Members and Foreign Associates Elected. In: Press release from the National Academy of Sciences (nasonline.org). April 29, 2014, accessed August 20, 2020 . 
2. ↑ Simon Baron-Cohen: Different from the first day. The female and male brain. Patmos, 2004, ISBN 3-530-42174-X , p. 212.