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Geometry, physics and the future of mathematics


Symplectic geometry
Michael Atiyah Mathematician
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Symplectic geometry in some sort of loose sense, you know, you hear it quite a lot and it floats around.  I'd been to Berkeley a lot where Weinstein talked about symplectic geometry and Kostant, MIT, talked about symplectic geometry. But it was all… most... most of that was at a fairly, sort of, formal elementary level, and nothing… I don't anything serious was going on.

So I think it probably was true that it was when I worked with Bott, that we... we got involved in it in a bit more serious way. And then I heard about… Mumford told me that what we were doing… how it fitted in with algebraic geometry, quotients and geometric invariant theory. And so it then began to become more seriously related with the topology and Frances Kirwan's work pushed it further. So I think it is true, that's the... that’s the first stage that I got involved with it. And of course the physicists… but then, when you talk to physicists, symplectic geometry is… well, I knew that it was… got of part of classical mechanics and is a kind of basis for quantum theory, but I'd never sort of played around with it in any serious way before myself; no, I think not.

Eminent British mathematician Sir Michael Atiyah (1929-2019) broke new ground in geometry and topology with his proof of the Atiyah-Singer Index Theorem in the 1960s. This proof led to new branches of mathematics being developed, including those needed to understand emerging theories like supergravity and string theory.

Listeners: Nigel Hitchin

Professor Nigel Hitchin, FRS, is the Rouse Ball Professor of Mathematics and Fellow of Gonville and Caius College, Cambridge, since 1994, and was appointed to the Savilian Professorship of Geometry in October 1997. He was made a Fellow of the Royal Society in 1991 and from 1994 until 1996 was President of the London Mathematical Society.

His research interests are in differential and algebraic geometry and its relationship with the equations of mathematical physics. He is particularly known for his work on instantons, magnetic monopoles, and integrable systems. In addition to numerous articles in academic journals, he has published "Monopoles, Minimal Surfaces and Algebraic Curves" (Presses de l'Universite de Montreal, 1987) and "The Geometry and Dynamics of Magnetic Monopoles" (Princeton University Press, 1988, with Michael Atiyah).

Tags: Berkeley, MIT, Alan Weinstein, Raoul Bott, David Mumford, Frances Kirwan

Duration: 1 minute, 4 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008