Nigel Hitchin

Nigel Hitchin James ( born August 2, 1946 in Holbrook, Derbyshire, England ) is an English mathematician who is engaged in differential geometry, algebraic geometry and mathematical physics.

Life and work

Nigel Hitchin studied from 1965 at Jesus College, Oxford, where in 1968 he earned his bachelor 's degree. In 1969 he received his diploma at Wolfson College, Oxford University, where he received his doctorate in 1972 with Michael Atiyah. 1971 to 1973 he was at the Institute for Advanced Study and in 1973/74 at the Courant Institute of Mathematical Sciences of New York University. After that, he was a Research Fellow at Oxford and from 1979 Tutor, Lecturer and Fellow of St Catherine 's College, Oxford. In 1990 he became a professor at the University of Warwick and from 1994 Rouse Ball Professor at Cambridge and Fellow of Gonville and Caius College. Since 1997 he has Savilian professor of geometry at Oxford (as successor of Atiyah ) and a Fellow of New College, Oxford.

Hitchin worked example of the relationship of integrable systems of mathematical physics with algebraic geometry, for example, in the Atiyah - Drinfeld - Hitchin - Manin construction ( ADHM construction ) of instantons of 1977 Atiyah, Yuri Manin, Vladimir Drinfeld (The construction of instantons. Physics Letters A, Vol 65, 1978, p.185 -187 ).

In 1974 he published the Hitchin - Thorpe inequality between the Euler characteristic and signature of a manifold M that must fulfill four-dimensional (smooth, compact ) manifolds which carry an Einstein metric: In the case of equality, he showed that M is a flat torus, a Calabi -Yau manifold or a quotient must be made of both.

In 1998 he was Honorary Fellow of Jesus College, Oxford. In 1991 he was elected to the Royal Society, which in 2000 awarded him the Sylvester Medal. 1994 to 1996 he was President of the London Mathematical Society, of which he Whitehead Prize, in 1990 the Senior Berwick Prize in 2002 and received the 1981 Pólya Prize.

Nigel Hitchin is editor of the journal Mathematische Annalen.

Among his students Simon Donaldson ( which he has edited with Atiyah ), Jacques Hurtubise and Simon Salamon.

In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw (The geometry of monopoles ).

Writings

• Monopole, minimal surfaces and algebraic curves. Montreal 1987.
• With Graeme Segal, Richard Ward: Integrable systems: Twistors, Loop Groups and Riemann surfaces. Oxford 1999.
• Global differential geometry, in Björn Engquist, Wilfried Schmid (Editor ) Mathematics Unlimited, Springer 2001