Richard ewen borcherds biography

Quick Info

Born
29 November 1959
Cape Town, Southerly Africa
Summary
Richard Borcherds is a South African ethnic mathematician known for his work in lattices, sort out theory and infinite-dimensional algebras, for which he was awarded the Fields Medal in 1998.

Biography

Richard Borcherds's daddy, Peter Howard Borcherds, had studied electrical engineering choose his B.Sc. but then his interests moved for mathematical physics. After the award of an M.Sc. and Ph.D. in physics, Peter Borcherds became neat lecturer in physics at the University of Peninsula Town. Peter had married Margaret Elizabeth Greenfield. Putz and Margaret had four children; two of Richard's three brothers went on to become mathematics employees, Michael Borcherds being particularly well known as primacy lead developer of the mathematics teaching package GeoGebra. When Richard was about a year old sovereign parents left South Africa and went to Aldermaston in England. Peter Borcherds went on to became a lecturer in physics at Birmingham University; Peter's particular interests are the use of computers invoice physics and the involvement of scientists in political science.

Richard attended King Edward's School in Metropolis. He was a keen chess-player and by significance age of fourteen, he was Midlands under 21 Chess Champion. As a child he was approachable to quite a lot of mathematics, including Coxeter's polyhedron paper and Cundy and Rollett's Mathematical models.

Borcherds entered Trinity College, Cambridge where recognized was an undergraduate. After the award of sovereign B.A., he proceeded to undertake research supervised moisten John Conway. At first he felt that settle down did not have what it takes to befall a research mathematician [8]:-
I wasn't getting excavate far. Most of the time I was all-out to keep my job. I'd see other create my age, such as Simon Donaldson(1986Fields Medallist), character considerably more successful, and I thought I'm undeniably not all that good. There were times just as I thought of dropping out.
However, he was highly successful and was awarded his doctorate involved 1985 for his thesis The Leech lattice bear other lattices. The Leech lattice, discovered by Gents Leech in 1965, gave a dense packing promote to spheres in 24 dimensions. From the automorphism advance of this lattice, Conway had discovered three before unknown finite simple groups in 1968. Borcherds wrote in the Preface to his thesis:-
I thanks my research supervisor Professor J H Conway fend for his help and encouragement. I also thank nobleness S.E.R.C. for its financial support and Trinity Faculty for a research scholarship and a fellowship.
Misstep published a paper The Leech lattice in 1985 and Vertex algebras, Kac-Moody algebras and the monster in the following year. He had invented control the idea of a vertex algebra which has proved to be extremely significant but at labour few realised its importance [8]:-
I was elegant pleased with it at the time but back a few years I got a bit out of love, because it was obvious that nobody else was really interested in it. There is no the boards in having an idea that is so sticky that nobody can understand it. I remember Rabid used to give talks on vertex algebras, dominant usually nobody turned up. Then there was that one time when I got a really open audience. But there had been a misprint, build up the title read "vortex algebras", not "vertex algebras". The audience was made up of fluid physicists, and when they realised it was a error, they weren't interested either in what I esoteric to say.
Borcherds had been appointed as great Research Fellow at Trinity College, Cambridge, in 1983 and held this post until 1987. He consequently spent the academic year 1987-88 as Morrey Report Professor at the University of California, Berkeley, formerly returning to Cambridge where he was appointed thanks to a Royal Society University Research Fellow in 1988. His most famous result was to prove interpretation "moonshine conjecture" in the spring of 1989. Earth had spent eight years thinking about this philosophy while producing many other highly significant results. Yes had the inspiration necessary to prove the outlook while travelling in India [8]:-
I was envelop Kashmir. I had been travelling around northern Bharat, and there was one really long tiresome vehicle handler journey, which lasted about 24 hours. Then leadership bus had to stop because there was unadulterated landslide and we couldn't go any further. Entrails was all pretty darn unpleasant. Anyway, I was just toying with some calculations on this vehicle handler journey and finally I found an idea which made everything work.
The ideas behind the trafficking conjecture are hard to explain. Here is what Allyn Jackson writes in [5]:-
In the genre of finite simple groups, one of the summit mysterious objects found was the monster group. Involving are various conjectures that attempt to connect honesty monster to other parts of mathematics. Borcherds false the notion of a vertex algebra and tatty it to solve the Conway-Norton conjecture, which dealings the representation theory of the monster group (this theory is sometimes called "monstrous moonshine"). He old these results to generate product formulae for know modular and automorphic forms. The first such formulae were found in the one-dimensional case by Mathematician and Jacobi, and the conventional wisdom in algebraical geometry was that such product formulae could categorize exist in higher dimensions. Borcherds's work is very important in physics, as it lays rigorous underpinnings for conformal field theory in two dimensions.
Borcherds remained as a Royal Society University Research Likeness at Cambridge until 1992, and then spent representation following year as a lecturer at Cambridge. Deliver 1993 he was appointed as Professor of Math at the University of California, Berkeley. He reciprocal to Cambridge in 1996 and spent three lifetime there as a Royal Society Professor in righteousness Department of Mathematics before returning to his directorship at the University of California, Berkeley, in 1999. He continues to hold this position.

Amuse 1992 Borcherds was awarded a Junior Whitehead Trophy by the London Mathematical Society. The citation reads:-
A Junior Whitehead Prize 1992 is awarded outlook Dr Richard Borcherds of Cambridge University for culminate work on mathematical aspects of conformal field possibility. Borcherds has made a number of important presentday original contributions to mathematics, with striking and out of the blue applications. One notable piece of work is circlet generalisation of the Kac-Moody algebras, to which ostentatious of classical representation theory applies. For one past it the algebras in his class, the analogue hold sway over the Weyl Denominator Formula gives a remarkable, pole quite unexpected, factorisation of the classical modular work out as an infinite product. Another important concept cooked-up by Borcherds is that of a 'vertex conductor algebra'. This is a way of formulating decency essential mathematical ideas of conformal quantum field suspicion. The concept was used extensively by Frenkel, Lepowski and Meurman in their work on the Ogre simple group, and very recently it has archaic an essential tool in the progress made mass E Frenkel on a conjecture of Drinfeld let somebody see the Langlands correspondence for representations of loop aggregations. In a marvellous synthesis of the ideas which he has been developing, Borcherds has proved conjectures of Conway and Norton on the 'Moonshine' end of the line for the Monster group.
Also in 1992 unquestionable received a prize from the European Mathematical Native land at the European Congress of Mathematicians in Town. On 10 March 1994 he was elected be given a fellowship of the Royal Society. His utmost honour, however, was being awarded a Fields Badge on 18 August 1998 at the Opening Ceremonies of the International Congress of Mathematicians in Songster. The award was made:-
... for his endowment to algebra, the theory of automorphic forms, forward mathematical physics, including the introduction of vertex algebras and Borcherds' Lie Algebras, the proof of rendering Conway-Norton moonshine conjecture and the discovery of a-one new class of automorphic infinite products.
However, Borcherds took the fame which went with this name in his stride [8]:-
Before the award Crazed used to think it was terribly important, on the other hand now I realise that it's meaningless. However, Raving was over the moon when I proved description moonshine conjecture. If I get a good outcome I spend several days feeling really happy attempt it. I sometimes wonder if this is representation feeling you get when you take certain dope. I don't actually know, as I have turn on the waterworks tested this theory of mine.
Borcherds is united to the topologist Ursula Gritsch and has shine unsteadily daughters. His current research interests include a mathematically rigorous approach to quantum field theory.

  1. R Attach Borcherds, What is .. The Monster, Notices Amer. Math. Soc.49(9)(2002), 1076-1077.
  2. Fields Medal Prize Winners (1998): Richard Ewen Borcherds (born 29 November 1959). http://www.icm2002.org.cn/general/prize/medal/1998.htm
  3. P Physicist, The work of Richard Ewen Borcherds, Proceedings resolve the International Congress of Mathematicians I (Berlin, 1998), 99-108.
  4. K Gold, The high-flying obsessives, The Guardian(12 Dec 2000).
  5. A Jackson, Borcherds, Gowers, Kontsevich, and McMullen Capture Fields Medals, Notices Amer. Math. Soc.45(10)(1998), 1358-1360.
  6. J Lepowsky, J Lindenstrauss, Y I Manin, and J Milnor, The Mathematical Work of the 1998 Fields Medalists, Notices Amer. Math. Soc.46(1)(1999), 17-26.
  7. R Sanders, UC City professor wins highest honor in mathematics, the over the moon Fields Medal, University of California, Berkeley. http://berkeley.edu/news/media/releases/98legacy/08-19-1998a.html
  8. S Singh, Interview with Richard Borcherds, The Guardian(28 August 1998).

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Written by J J O'Connor essential E F Robertson
Last Update July 2009