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Starting to understand harmonic integrals


Background to differential geometry
Michael Atiyah Mathematician
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I went to the topology courses. You know, people – Hilton and Wylie gave courses on algebraic topology – and so I did quite a bit of that, which was helpful background to the sort of differential geometry – global differential geometry – that Hodge did. Characteristic classes were just in the air and so it wasn't a single subject, there was a bit of back up on the topology side. But I didn't know much differential geometry. I'd been to a course he gave on Riemannian geometry, I suppose. But it was… and once you start you do research, of course there are all sorts of difficulties you know, everybody has. It was certainly different from what you… it was a quantum jump from what you did as an undergraduate, the kind of geometry there to what he was doing. He was going a bit into, sort of, unknown waters. The topology gave one a bit of a clue, but otherwise it was a bit of a gamble, yes.

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: topology, differential geometry, elective subjects, Riemannian geometry

Duration: 54 seconds

Date story recorded: March 1997

Date story went live: 24 January 2008