View source for Nigel Hitchin

{{short description|British mathematician}}
{{Use British English|date=July 2017}}
{{Use dmy dates|date=July 2017}}
{{Infobox scientist
| name              = Nigel Hitchin
| image             = Hitchin70.jpg
| caption           = Hitchin in 2016
| birth_date        = {{Birth date and age|df=yes|1946|08|02}}
| birth_place       = [[Holbrook, Derbyshire]], England
| death_date        = 
| death_place       = 
| nationality       = British
| field             = [[Mathematics]]
| work_institutions = [[University of Oxford]]<br>[[University of Warwick]]<br>[[University of Cambridge]]
| doctoral_advisor  = [[Brian Steer]]<br>[[Michael Atiyah]]
| doctoral_students = [[Simon Donaldson]]<br>[[Oscar Garcia Prada]]<br>[[Tamás Hausel]]<br>[[Jacques Hurtubise (mathematician)|Jacques Hurtubise]]<ref name="MGP">{{MathGenealogy|id=43911|name=Nigel James Hitchin}}<br>Oscar Garcia Prada</ref>
| known_for         = [[Higgs bundle]]<br>[[ADHM construction]]<br>[[Atiyah–Hitchin–Singer theorem]]<br>[[Hitchin functional]]<br> [[Hitchin's equations]]<br>[[Hitchin–Thorpe inequality]]<br>[[Kobayashi–Hitchin correspondence]]<br>[[Nahm equations#Nahm–Hitchin description of monopoles|Nahm–Hitchin description of monopoles]]<br>[[Generalized complex structure]]
| awards            = [[Whitehead Prize]] {{small|(1981)}}<br>[[Senior Berwick Prize]] <small>(1990)</small><br>[[Sylvester Medal]] <small>(2000)</small><br>[[Pólya Prize (LMS)|Pólya Prize]] <small>(2002)</small><br>[[Shaw Prize]] <small>(2016)</small>
| education         = [[Jesus College, Oxford]] ([[Bachelor of Arts|BA]])<br>[[Wolfson College, Oxford]] ([[DPhil]])
}}
'''Nigel James Hitchin''' [[Fellow of the Royal Society|FRS]] (born 2 August 1946) is a British mathematician working in the fields of [[differential geometry]], [[gauge theory (mathematics)|gauge theory]], [[algebraic geometry]], and [[mathematical physics]]. He is a Professor Emeritus of Mathematics at the [[University of Oxford]].

==Academic career==
Hitchin attended [[Ecclesbourne School]], [[Duffield, Derbyshire|Duffield]], and earned his [[Bachelor of Arts|BA]] in mathematics from [[Jesus College, Oxford]], in 1968.<ref name=Jesus>''Fellows' News'', Jesus College Record (1998/9) (p.12)</ref> After moving to [[Wolfson College, Oxford|Wolfson College]], he received his [[Doctor of Philosophy|D.Phil.]] in 1972. From 1971 to 1973 he visited the [[Institute for Advanced Study]] and 1973/74 the [[Courant Institute of Mathematical Sciences]] of [[New York University]]. He then was a research fellow in Oxford and starting in 1979 tutor, lecturer and fellow of [[St Catherine's College, Oxford|St Catherine's College]]. In 1990 he became a professor at the [[University of Warwick]] and in 1994 the [[Rouse Ball Professor of Mathematics]] at the [[University of Cambridge]]. In 1997 he was appointed to the [[Savilian Professor of Geometry|Savilian Chair of Geometry]] at the [[University of Oxford]], a position he held until his retirement in 2016.

Amongst his notable discoveries are the [[Hitchin&ndash;Thorpe inequality]]; Hitchin's [[Projective differential geometry|projectively]] [[flat connection]] over [[Teichmüller space]]; the Atiyah–Hitchin monopole metric; the [[Atiyah–Hitchin–Singer theorem]]; the [[ADHM construction]] of [[instanton]]s (of [[Michael Atiyah]], [[Vladimir Drinfeld]], Hitchin, and [[Yuri Manin]]); the [[hyperkähler quotient]] (of Hitchin, Anders Karlhede, [[Ulf Lindström]] and [[Martin Roček]]); [[Higgs bundle]]s, which arise as solutions to the Hitchin equations, a 2-dimensional reduction of the self-dual [[Yang–Mills theory|Yang–Mills equations]]; and the [[Hitchin system]], an algebraically [[integrable system|completely integrable Hamiltonian system]] associated to the data of an [[algebraic curve]] and a complex [[reductive group]].  He and [[Shoshichi Kobayashi]] independently conjectured the [[Kobayashi–Hitchin correspondence]].  Higgs bundles, which are also developed in the work of [[Carlos Simpson]], are closely related to the Hitchin system, which has an interpretation as a [[moduli space]] of semistable Higgs bundles over a compact [[Riemann surface]] or algebraic curve.<ref name="plms">{{cite journal|first=Nigel J.|last= Hitchin|title=The self-duality equations on a Riemann surface|journal= [[London Mathematical Society|Proceedings of the London Mathematical Society]]|volume= 55|issue=1|year= 1987|pages= 59–126|doi=10.1112/plms/s3-55.1.59|mr=0887284}}</ref>  This moduli space has emerged as a focal point for deep connections between algebraic geometry, differential geometry, [[hyperkähler manifold|hyperkähler geometry]], mathematical physics, and [[representation theory]].

In his article<ref name=gCYm>{{Citation |last=Hitchin |first=Nigel |title=Generalized Calabi–Yau manifolds |journal=[[Quarterly Journal of Mathematics]] |volume=54 |year=2003 |issue=3 |pages=281–308 |arxiv=math/0209099v1  |doi=10.1093/qmath/hag025 }}</ref> on generalized [[Calabi–Yau manifold]]s, he introduced the notion of [[Generalized complex structure|generalized complex manifold]]s, 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 [[Compactification (physics)#Flux compactification|flux compactification]]s in [[string theory]] and also in [[topological string theory]].

In the span of his career, Hitchin has supervised 37 research students, including [[Simon Donaldson]] (part-supervised with Atiyah).

Until 2013 Nigel Hitchin served as the managing editor of the journal ''[[Mathematische Annalen]]''.

==Honours and awards==

In 1991 he was elected a [[Fellow of the Royal Society]].<ref>{{cite web | url= http://royalsociety.org/about-us/fellowship/fellows/|title = fellows| publisher = Royal Society|access-date = 20 November 2010}}</ref>

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

Hitchin was elected as an [[List of Honorary Fellows of Jesus College, Oxford|Honorary Fellow of Jesus College]] in 1998,<ref name=Jesus/> and the [[Berwick Prizes|Senior Berwick Prize]] (1990), the [[Sylvester Medal]] (2000) and the [[Pólya Prize (LMS)|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 2012 he became a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society]. Retrieved 21 January 2013.</ref> In 2014 he was awarded another Honorary Degree (Doctor of Science) from the [[University of Warwick]]. In 2016 he received the [[Shaw Prize]] in Mathematical Sciences.<ref>{{Cite web |url=http://www.shawprize.org/en/shaw.php?tmp=3&twoid=102&threeid=256&fourid=466 |title=Shaw Prize 2016 |access-date=31 May 2016 |archive-date=19 October 2016 |archive-url=https://web.archive.org/web/20161019210510/http://www.shawprize.org/en/shaw.php?tmp=3&twoid=102&threeid=256&fourid=466 |url-status=dead }}</ref>

==References==
{{reflist|30em}}

==External links==
*[http://people.maths.ox.ac.uk/hitchin/ His home page at the University of Oxford]
*{{MathGenealogy |id=43911}}

{{FRS 1991}}
{{Shaw Prize laureates}}
{{Savilian Professors of Geometry}}
{{Authority control}}

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