HITCHIN, NIGEL / Mathematics / Researchers

International Center for Scientific Research

Researchers

Mathematics / HITCHIN, NIGEL

Hitchinmaths.ox.ac.uk

Position

Savilian Professor of Geometry, Mathematical Institute, University of Oxford, Great Britain.

Professorial Fellow, New College

Research interests

Differential and algebraic geometry and its relationship with the equations of mathematical physics.

Current projects include the areas of :
- Hyperk®ahler geometry
- Special Lagrangian geometry and mirror symmetry
- Geometric solutions of Painlev¥e equations
- Magnetic monopoles
- Vector bundles on algebraic curves
- The theory of gerbes

Prizes and awards

2003 : Honorary DSc University of Bath
2002 : London Mathematical Society Polya Prize
2000 : Sylvester Medal of the Royal Society
1998 : Honorary Fellow, Jesus College, Oxford
1991 : Fellow of the Royal Society
1990 : London Mathematical Society Senior Berwick Prize
1981 : London Mathematical Society Junior Whitehead Prize
1968 : Oxford University Junior Mathematical Prize


Learned societies :

- Academia Europea
- American Mathematical Society
- European Mathematical Society
- London Mathematical Society
- Royal Society

Publications

with S. Cherkis), Gravitational instantons of type D_k.

What is a gerbe? Notices of the AMS, 50 No 2 (2003), 218 -- 219.

A lecture on the octahedron , Bulletin of the London Math Soc, 35 (2003) 577--600.

Special holonomy and beyond, in ``Strings and Geometry", M. Douglas, J. Gauntlett M. Gross (eds.), Clay Mathematics Proceedings Vol 3, American Mathematical Society, Providence (2005)

Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford, 54 (2003) 281--308.

Stable forms and special metrics, in "Global Differential Geometry: The Mathematical Legacy of Alfred Gray";, M. Fernández and J. A. Wolf (eds.), Contemporary Mathematics 288, American Mathematical Society, Providence (2001).

The geometry of three-forms in six dimensions, J. Differential Geometry 55 (2000), 547 - 576.

The Wess-Zumino term for a harmonic map, Journal für die reine und angewandte Mathematik 543 (2002) 83 -101.

Global Differential Geometry, in " Mathematics Unlimited - 2001 and Beyond", (B.Enquist and W.Schmid (Eds)), Springer Verlag, Heidelberg (2000) 577 - 591.

Sir Michael Atiyah: a brief biography in "The Founders of Index Theory", S-T Yau (ed.), International Press, Boston (2004)

cohomology of hyperkähler quotients. Commun. Math. Phys. 211 (2000), 153 -165.

(with Justin Sawon) Curvature and characteristic numbers of hyperkähler manifolds, Duke Mathematical Journal 106 (2001), 599 - 615.

Lectures on special Lagrangian submanifolds, in " Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds" ;, Cumrun Vafa & S-T Yau (eds.), Studies in Advanced Mathematics 23, AMS/International Press, Providence (2001), 151 - 182.

The Dirac operator, in " Invitations to Geometry and Topology'', M.Bridson and S.Salamon (eds.), Oxford Graduate Texts in Mathematics, Oxford University Press, Oxford (2002), 208 - 232.

(with G.B.Segal and R.S.Ward) " Integrable systems: Twistors, loop groups and Riemann surfaces'', Oxford Graduate Texts in Mathematics, Oxford University Press , Oxford (1999).

The moduli space of complex Lagrangian submanifolds, Asian Journal of Mathematics, 3 (1999) 77 - 92.

Integrable systems in Riemannian geometry, in " Surveys in Differential Geometry Vol. 4'', C.-L. Terng and K. Uhlenbeck, (eds.), International Press, Cambridge, Mass. (1999), 21 - 80.

Hypercomplex manifolds and the space of framings, in " The Geometric Universe: Science, Geometry and the work of Roger Penrose'', S.A.Huggett et al (eds.), Oxford University Press, Oxford, (1998), 9 - 30.

The moduli space of special Lagrangian submanifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997), no. 3 - 4, 503 - 515

Geometrical aspects of Schlesinger's equation, Journal of Geometry and Physics 457 (1997), 1 - 14.

Lectures on Frobenius manifolds, in " Gauge Theory and Symplectic Geometry'', J.Hurtubise & F.Lalonde (eds), NATO ASI Series C 488, Kluwer, Dordrecht (1997).

Einstein metrics and the eta-invariant, Bollettino UMI (7) 11-B Suppl. fasc. 2 (1997), 95 - 105.

Magnetic monopoles with Platonic symmetry, in " Moduli of vector bundles (Sanda, 1994; Kyoto, 1994)'', 55 - 63, Lecture Notes in Pure and Appl. Math., 179, Dekker, New York, 1996.

A new family of Einstein metrics, in " Manifolds and geometry (Pisa, 1993)'', 190 - 222, Sympos. Math., XXXVI, Cambridge Univ. Press, Cambridge, 1996.

Poncelet polygons and the Painlevé equations, in " Geometry and analysis (Bombay, 1992)'', 151 - 85, Oxford University Press, Bombay, 1996.

(with N S Manton and M K Murray) Symmetric monopoles, Nonlinearity 8 (1995), 661 - 692.

Twistor spaces, Einstein metrics and isomonodromic deformations, J. Differential Geom. 42 (1995), 30 - 112.

" Vector bundles in algebraic geometry.'' Proceedings of the symposium held in Durham, 1993. Edited by N. J. Hitchin, P. E. Newstead and W. M. Oxbury. London Mathematical Society Lecture Note Series, 208. Cambridge University Press, Cambridge, 1995. +345 pp. ISBN: 0-521-49878-3

Hyperkähler manifolds, Séminaire Bourbaki, Vol. 1991/92. Astérisque No. 206 (1992), Exp. No. 748, 3, 137-166.

Lie groups and Teichmüller space, Topology 31 (1992), 449 - 473.

The symplectic geometry of moduli spaces of connections and geometric quantization, in " Common trends in mathematics and quantum field theories (Kyoto, 1990).'' Progr. Theoret. Phys. Suppl. No. 102, (1991), 159 - 174.

(with M F Atiyah) " Geometriya i dinamika magnitnykh monopolei''. (Russian) [The geometry and dynamics of magnetic monopoles] Translated from the English and with a preface by O. V. Ogievetskii. " Mir'', Moscow, (1991).

Vector fields on the circle, in " Mechanics, analysis and geometry: 200 years after Lagrange'', North-Holland Delta Ser., North-Holland, Amsterdam, (1991), 359 - 378.

Geometric quantization of spaces of connections, in " Geometry of low-dimensional manifolds, 2 (Durham, 1989)'', London Math. Soc. Lecture Note Ser., 151, Cambridge Univ. Press, Cambridge, (1990) 97 - 100.

Hypersymplectic quotients, Atti della Accademia delle Scienze di Torino, Classe di Scienze Fisiche, Matematiche e Naturali, 124 Supp. (1990), 169 - 180.

The geometry and topology of moduli spaces, in " Global geometry and mathematical physics (Montecatini Terme, 1988)'', Lecture Notes in Math., 1451, Springer, Berlin, (1990), 1-48.

Flat connections and geometric quantization, Comm. Math. Phys. 131 (1990), 347-380.

Harmonic maps from a 2-torus to the 3-sphere, J. Differential Geom. 31 (1990), 627-710.

Gauge theory on Riemann surfaces, in " Lectures on Riemann surfaces (Trieste, 1987)'', 99-118, World Sci. Publishing, Teaneck, NJ, 1989.

Harmonic maps from to , in " Harmonic mappings, twistors, and -models (Luminy, 1986)'', 103-112, Adv. Ser. Math. Phys., 4, World Sci. Publishing, Singapore, 1988.

(with M F Atiyah) " The geometry and dynamics of magnetic monopoles.'' M. B. Porter Lectures. Princeton University Press, Princeton, NJ, 1988. viii+134 pp. ISBN: 0-691-08480-7

" Monopoles, minimal surfaces and algebraic curves.'' Séminaire de Mathématiques Supérieures, Presses de l'Université de Montréal, Montreal, PQ, 1987. 94 pp. ISBN: 2-7606-0801-8

(with M K Murray) Spectral curves and the ADHM method, Comm. Math. Phys. 114 (1988), 463-474.

The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), 59-126.

Stable bundles and integrable systems, Duke Math. J. 54 (1987), 91-114.

Monopole and vortex scattering, in " Field theory, quantum gravity and strings, II (Meudon/Paris, 1985/1986)'', 117-124, Lecture Notes in Phys., 280, Springer, Berlin-New York, (1987).

(with A. Karlhede, U. Lindström, M. Rocek) Hyperkähler metrics and supersymmetry, Comm. Math. Phys. 108 (1987), 535-589.

Metrics on moduli spaces, in " The Lefschetz centennial conference, Part I (Mexico City, 1984)'', 157-178, Contemp. Math., 58, Amer. Math. Soc., Providence, R.I., 1986.

(with M F Atiyah) Low-energy scattering of nonabelian magnetic monopoles, in " New developments in the theory and application of solitons. With discussion.'' Philos. Trans. Roy. Soc. London Ser. A 315 (1985), no. 1533, 459-469.

(with M F Atiyah) Low energy scattering of nonabelian monopoles, Phys. Lett. A 107 (1985), 21-25.

The geometry of monopoles, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 541-547, PWN, Warsaw, 1984.

Twistor construction of Einstein metrics, in " Global Riemannian geometry'' (Durham, 1983), 115-125, Ellis Horwood Ser.: Math. Appl., Horwood, Chichester, 1984.

" Global Riemannian geometry''. Proceedings of the symposium held at the University of Durham, Durham, July 1983. Edited by T. J. Willmore and N. J. Hitchin. Ellis Horwood Series: Mathematics and its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, 1984.

The Yang-Mills equations and the topology of 4-manifolds (after Simon Donaldson), Bourbaki seminar vol 1982/83, 167-178, Astérisque 105-106, Soc. Math. France, Paris (1983).

On the construction of monopoles, Commun. Math. Phys. 89 (1983) 145-190.

Monopoles and geodesics, Commun. Math. Phys. 83 (1982) 579-602.

Complex manifolds and Einstein's equations, in " Twistor geometry and nonlinear systems'' , H.Doebner et al (Eds), Lecture Notes in Mathematics 970, 73-99, Springer, Berlin (1982).

Kählerian twistor spaces, Proc. London Math. Soc. 43 (1981), 133-150.

Linear field equations on self-dual spaces, Proc. Roy. Soc. London Ser. A 370 (1980), 173-191.

(with M F Atiyah, V G Drinfeld, Yu I Manin) Construction of instantons, Phys. Lett. A 65 (1978), 185-187.

Polygons and gravitons, Math. Proc. Camb. Phil. Soc. 85 (1979), 465-476.

(with M F Atiyah, I M Singer) Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser A 362 (1978), 425-461.

(with M F Atiyah, I M Singer) Deformations of instantons, Proc. Nat. Acad. Sci. USA (1977) 7, 2662-2663.

On the curvature of rational surfaces, Proc. Sympos. Pure Math. XXVII, pp 65-80, Amer. Math. Soc. Providence RI (1975)

Harmonic spinors, Advances in Mathematics 14 (1974), 1-55.

Compact four-dimensional Einstein manifolds, J.Differential Geometry 9 (1974), 435-441.

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