Nigel Hitchin
Encyclopedia
Nigel Hitchin is a British
mathematician
working in the fields of differential geometry, algebraic geometry
, and mathematical physics
.
in mathematics from Jesus College, Oxford
in 1968. After moving to Wolfson College
, he received his D.Phil.
in 1972. In 1997 he was appointed to the Savilian Chair of Geometry
at Oxford University, a position previously held by his doctoral supervisor (and later research collaborator) Sir Michael Atiyah
.
Amongst his notable discoveries are the Hitchin integrable system
, the Hitchin–Thorpe inequality, Hitchin's projectively
flat connection over Teichmüller space
, Hitchin's self-duality equations, the Atiyah-Hitchin monopole metric, the ADHM construction
of instanton
s (of Atiyah, Drinfeld
, Hitchin, and Manin
), and the hyperkähler quotient construction (of Hitchin, Karlhede, Lindström
and Rocek
).
In his article on generalized Calabi-Yau manifold
s, he introduced the notion of generalized complex manifolds, providing a single structure that incorporates, as examples, Poisson manifold
s, symplectic manifold
s and complex manifold
s. These have found wide applications as the geometries of flux compactifications in string theory
and also in topological string theory
.
Hitchin was elected as an Honorary Fellow of Oxford's Jesus College in 1998, and the Senior Berwick Prize
(1990), the Sylvester Medal
(2000) and the Pólya Prize
(2002) have been awarded to him in honour of his far-reaching work. A conference was held in honour of his 60th birthday, in conjunction with the 2006 International Congress of Mathematicians
in Spain.
In the span of his career, Hitchin has supervised nearly thirty research students, including Simon Donaldson
(part-supervised with Atiyah).
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working in the fields of differential geometry, algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, and mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
.
Academic career
Hitchin attended Ecclesbourne School, Duffield, and earned his BABachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in mathematics from Jesus College, Oxford
Jesus College, Oxford
Jesus College is one of the colleges of the University of Oxford in England. It is in the centre of the city, on a site between Turl Street, Ship Street, Cornmarket Street and Market Street...
in 1968. After moving to Wolfson College
Wolfson College, Oxford
Wolfson College is a constituent college of the University of Oxford in England. Located in north Oxford along the River Cherwell, Wolfson is an all-graduate college with over sixty governing body fellows, in addition to both research and junior research fellows. It caters to a wide range of...
, he received his D.Phil.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1972. In 1997 he was appointed to the Savilian Chair of Geometry
Savilian Professor of Geometry
The position of Savilian Professor of Geometry was established at the University of Oxford in 1619. It was founded by Sir Henry Savile, a mathematician and classical scholar who was Warden of Merton College, Oxford and Provost of Eton College, reacting to what has been described as "the wretched...
at Oxford University, a position previously held by his doctoral supervisor (and later research collaborator) Sir Michael Atiyah
Michael Atiyah
Sir Michael Francis Atiyah, OM, FRS, FRSE is a British mathematician working in geometry.Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study...
.
Amongst his notable discoveries are the Hitchin integrable system
Hitchin system
In mathematics, the Hitchin integrable system is an integrable system introduced by Nigel Hitchin in 1987. It lies on the crossroadsof the algebraic geometry, theory of Lie algebras and integrable system theory...
, the Hitchin–Thorpe inequality, Hitchin's projectively
Projective differential geometry
In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties that are invariant under the projective group. This is a mixture of attitudes from Riemannian geometry, and the Erlangen program....
flat connection over Teichmüller space
Teichmüller space
In mathematics, the Teichmüller space TX of a topological surface X, is a space that parameterizes complex structures on X up to the action of homeomorphisms that are isotopic to the identity homeomorphism...
, Hitchin's self-duality equations, the Atiyah-Hitchin monopole metric, the ADHM construction
ADHM construction
The ADHM construction or monad construction is the construction of all instantons using method of linear algebra by Michael Atiyah, Vladimir G. Drinfel'd, Nigel. J. Hitchin, Yuri I...
of instanton
Instanton
An instanton is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory...
s (of Atiyah, Drinfeld
Vladimir Drinfel'd
Vladimir Gershonovich Drinfel'd is a Ukrainian and Soviet mathematician at the University of Chicago.The work of Drinfeld related algebraic geometry over finite fields with number theory, especially the theory of automorphic forms, through the notions of elliptic module and the theory of the...
, Hitchin, and Manin
Yuri I. Manin
Yuri Ivanovitch Manin is a Soviet/Russian/German mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.-Biography:...
), and the hyperkähler quotient construction (of Hitchin, Karlhede, Lindström
Ulf Lindstrom
Ulf Lindström is a Swedish theoretical physicist working in the fields of string theory, supersymmetry, and general relativity....
and Rocek
Martin Rocek
Martin Rocek is a professor of theoretical physics at the State University of New York at Stony Brook and a member of the C. N. Yang Institute for Theoretical Physics. He received A.B. and Ph.D. degrees from Harvard University in 1975 and 1979...
).
In his article on generalized Calabi-Yau manifold
Calabi-Yau manifold
A Calabi-Yau manifold is a special type of manifold that shows up in certain branches of mathematics such as algebraic geometry, as well as in theoretical physics...
s, he introduced the notion of generalized complex manifolds, providing a single structure that incorporates, as examples, Poisson manifold
Poisson manifold
In mathematics, a Poisson manifold is a differentiable manifold M such that the algebra C^\infty\, of smooth functions over M is equipped with a bilinear map called the Poisson bracket, turning it into a Poisson algebra...
s, symplectic manifold
Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology...
s and complex manifold
Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic....
s. These have found wide applications as the geometries of flux compactifications in string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
and also in topological string theory
Topological string theory
In theoretical physics, topological string theory is a simplified version of string theory. The operators in topological string theory represent the algebra of operators in the full string theory that preserve a certain amount of supersymmetry...
.
Honours and Awards
In 1991 he was elected a Fellow of the Royal Society.Hitchin was elected as an Honorary Fellow of Oxford's Jesus College in 1998, and the Senior Berwick Prize
Berwick Prizes
The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the society to establish two prizes...
(1990), the Sylvester Medal
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize...
(2000) and the Pólya Prize
Pólya Prize (LMS)
The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in which the De Morgan Medal is not awarded...
(2002) have been awarded to him in honour of his far-reaching work. A conference was held in honour of his 60th birthday, in conjunction with the 2006 International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in Spain.
In the span of his career, Hitchin has supervised nearly thirty research students, including Simon Donaldson
Simon Donaldson
Simon Kirwan Donaldson FRS , is an English mathematician known for his work on the topology of smooth four-dimensional manifolds. He is now Royal Society research professor in Pure Mathematics and President of the Institute for Mathematical Science at Imperial College London...
(part-supervised with Atiyah).