Hitchin attended
Ecclesbourne School,
Duffield, and earned his
BA in mathematics from
Jesus College, Oxford, in 1968. After moving to
Wolfson College, he received his
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. 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 Chair of Geometry at the
University of Oxford, a position he held until his retirement in 2016. Amongst his notable discoveries are the
Hitchin–Thorpe inequality; Hitchin's
projectively flat connection over
Teichmüller space; the Atiyah–Hitchin monopole metric; the
Atiyah–Hitchin–Singer theorem; the
ADHM construction of
instantons (of
Michael Atiyah,
Vladimir Drinfeld, Hitchin, and
Yuri Manin); the
hyperkähler quotient (of Hitchin, Anders Karlhede,
Ulf Lindström and
Martin Roček);
Higgs bundles, which arise as solutions to the Hitchin equations, a 2-dimensional reduction of the self-dual
Yang–Mills equations; and the
Hitchin system, an algebraically
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. This moduli space has emerged as a focal point for deep connections between algebraic geometry, differential geometry,
hyperkähler geometry, mathematical physics, and
representation theory. In his article on generalized
Calabi–Yau manifolds, he introduced the notion of
generalized complex manifolds, providing a single structure that incorporates, as examples,
Poisson manifolds,
symplectic manifolds and
complex manifolds. These have found wide applications as the geometries of
flux compactifications 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==