Nigel James Hitchin FRS (born 2 August 1946) is a British mathematician working in the fields of

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups) ...

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, and

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

. He is a Professor Emeritus of Mathematics at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

Academic career

Hitchin attended Ecclesbourne School, Duffield, and earned his BA in mathematics from

Jesus College, Oxford Jesus College (in full: Jesus College in the University of Oxford of Queen Elizabeth's Foundation) is one of the constituent colleges of the University of Oxford in England. It is in the centre of the city, on a site between Turl Street, Ship St ...

, in 1968.''Fellows' News'', Jesus College Record (1998/9) (p.12) After moving to Wolfson College, he received his

D.Phil. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1972. From 1971 to 1973 he visited the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

and 1973/74 the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

. He then was a research fellow in Oxford and starting in 1979 tutor, lecturer and fellow of St Catherine's College. In 1990 he became a professor at the

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands (county), West Midlands and Warwickshire, England. The university was founded i ...

and in 1994 the

Rouse Ball Professor of Mathematics The Rouse Ball Professorship of Mathematics is one of the senior chairs in the Mathematics Departments at the University of Cambridge and the University of Oxford. The two positions were founded in 1927 by a bequest from the mathematician W. W. Ro ...

at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. In 1997 he was appointed to the

Savilian Chair of Geometry The position of Savilian Professor of Geometry was established at the University of Oxford in 1619. It was founded (at the same time as the Savilian Professorship of Astronomy) by Sir Henry Savile, a mathematician and classical scholar who was ...

at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

, a position he held until his retirement in 2016. Amongst his notable discoveries are the Hitchin–Thorpe inequality; Hitchin's projectively

flat connection In differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry can be considered as a special case. Definition Let ''G'' be a Lie group with Lie alge ...

over

Teichmüller space In mathematics, the Teichmüller space T(S) of a (real) topological (or differential) surface S, is a space that parametrizes complex structures on S up to the action of homeomorphisms that are isotopic to the identity homeomorphism. Teichmülle ...

; the Atiyah–Hitchin monopole metric; the

Atiyah–Hitchin–Singer theorem In differential geometry and gauge theory, the Atiyah–Hitchin–Singer theorem, introduced by , states that the space of SU(2) anti self dual Yang–Mills fields on a 4-sphere with index Index (or its plural form indices) may refer to: Arts, ...

; the

ADHM construction In mathematical physics and gauge theory, the ADHM construction or monad construction is the construction of all instantons using methods of linear algebra by Michael Atiyah, Vladimir Drinfeld, Nigel Hitchin, Yuri I. Manin in their paper "Constru ...

instanton An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. Mo ...

s (of

Michael Atiyah Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...

Vladimir Drinfeld Vladimir Gershonovich Drinfeld ( uk, Володи́мир Ге́ршонович Дрінфельд; russian: Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a renowne ...

, Hitchin, and

Yuri Manin Yuri Ivanovich Manin (russian: Ю́рий Ива́нович Ма́нин; born 16 February 1937) is a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logi ...

); the hyperkähler quotient (of Hitchin, Anders Karlhede,

Ulf Lindström Ulf Lindström (born 12 November 1947) is a Swedish theoretical physicist working in the fields of string theory, supersymmetry, and general relativity. He earned his fil. kand. university degree at Stockholm University in 1972 and continued un ...

and Martin Roček);

Higgs bundle In mathematics, a Higgs bundle is a pair (E,\varphi) consisting of a holomorphic vector bundle ''E'' and a Higgs field \varphi, a holomorphic 1-form taking values in the bundle of endomorphisms of ''E'' such that \varphi \wedge \varphi=0. Such pai ...

s, which arise as solutions to the Hitchin equations, a 2-dimensional reduction of the self-dual

Yang–Mills equations In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the E ...

; and the

Hitchin system In mathematics, the Hitchin integrable system is an integrable system depending on the choice of a complex reductive group and a compact Riemann surface, introduced by Nigel Hitchin in 1987. It lies on the crossroads of algebraic geometry, the th ...

, an algebraically completely integrable Hamiltonian system associated to the data of an

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane c ...

and a complex

reductive group In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group ''G'' over a perfect field is reductive if it has a representation with finite kernel which is a direct ...

. He and

Shoshichi Kobayashi was a Japanese mathematician. He was the eldest brother of electrical engineer and computer scientist Hisashi Kobayashi. His research interests were in Riemannian and complex manifolds, transformation groups of geometric structures, and Lie alge ...

independently conjectured the

Kobayashi–Hitchin correspondence In differential geometry, algebraic geometry, and gauge theory, the Kobayashi–Hitchin correspondence (or Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The co ...

. Higgs bundles, which are also developed in the work of

Carlos Simpson Carlos Tschudi Simpson (born 30 June 1962) is an American mathematician, specializing in algebraic geometry. Simpson received his Ph.D. in 1987 from Harvard University, where he was supervised by Wilfried Schmid; his thesis was titled ''Systems of ...

, are closely related to the Hitchin system, which has an interpretation as a

moduli space In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spac ...

of semistable Higgs bundles over a compact

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

or algebraic curve. This moduli space has emerged as a focal point for deep connections between algebraic geometry, differential geometry, hyperkähler geometry, mathematical physics, and

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

. In his article on generalized

Calabi–Yau manifold In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring ...

s, he introduced the notion of generalized complex manifolds, providing a single structure that incorporates, as examples,

Poisson manifold In differential geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M , subject to the Leibniz rule : \ = \h + g \ . Equivalentl ...

symplectic manifold In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M , equipped with a closed nondegenerate differential 2-form \omega , called the symplectic form. The study of symplectic manifolds is called sympl ...

s and

complex manifold In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in \mathbb^n, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a com ...

s. These have found wide applications as the geometries of flux compactifications in

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...

and also in

topological string theory In theoretical physics, topological string theory is a version of string theory. Topological string theory appeared in papers by theoretical physicists, such as Edward Witten and Cumrun Vafa, by analogy with Witten's earlier idea of topological qu ...

. In the span of his career, Hitchin has supervised 37 research students, including

Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He i ...

(part-supervised with Atiyah). Until 2013 Nigel Hitchin served as the managing editor of the journal ''

Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...

''.

Honours and awards

In 1991 he was elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

. In 2003 he was awarded an Honorary Degree (Doctor of Science) from the

University of Bath (Virgil, Georgics II) , mottoeng = Learn the culture proper to each after its kind , established = 1886 (Merchant Venturers Technical College) 1960 (Bristol College of Science and Technology) 1966 (Bath University of Technology) 1971 (univ ...

. Hitchin was elected as an Honorary Fellow of Jesus College in 1998, and the

Senior Berwick Prize 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 s ...

(1990), the

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...

(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 The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Spain. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 2014 he was awarded another Honorary Degree (Doctor of Science) from the

. In 2016 he received the

Shaw Prize The Shaw Prize is an annual award presented by the Shaw Prize Foundation. Established in 2002 in Hong Kong, it honours "individuals who are currently active in their respective fields and who have recently achieved distinguished and signifi ...

in Mathematical Sciences.Shaw Prize 2016
/ref>

References

External links

His home page at the University of Oxford
* {{DEFAULTSORT:Hitchin, Nigel 1946 births Living people People from Holbrook, Derbyshire 20th-century English mathematicians 21st-century English mathematicians Differential geometers Alumni of Jesus College, Oxford Alumni of Wolfson College, Oxford Savilian Professors of Geometry Whitehead Prize winners Fellows of New College, Oxford Fellows of the Royal Society Fellows of the American Mathematical Society Rouse Ball Professors of Mathematics (Cambridge) Academics of the University of Warwick