Publications of Nigel Hitchin
109. ALE spaces and nodal curves arXiv:2402.04021
108. (with A. Beauville, O. Garcia-Prada, C. Khare, S. Kumar (Editor), H. Lange, N. Nitsure, M. S. Raghunathan, T. R. Ramadas, and S. Ramanan) Remembering M. S. Narasimhan (1932–2021), Notices Amer. Math. Soc. 69 (2022), no. 7, 1189–1203.
107. A note on coupled Dirac operators, SIGMA Symmetry Integrability Geom. Methods Appl. 19 (2023), Paper No. 003, 9 pp, arXiv:2210.17512
106. Multiplicity algebras for rank 2 bundles on curves of small genus, arXiv:2203.03424
105. A remark on calibrations and Lie groups, arXiv:2201.06331
104. Spinors, twistors and classical geometry, SIGMA Symmetry Integrability Geom. Methods Appl. 17 (2021), Paper No. 090, 9 pp, arXiv:2108.02603
103. (with T. Hausel) Very stable Higgs bundles, equivariant multiplicity and mirror symmetry, Invent. Math. 228 (2022), no. 2, 893–989, arXiv:2101.08583
102. A Teichmüller space for negatively curved surfaces, Proc. Lond. Math. Soc. (3) 126 (2023), no.3, 900–922, arXiv:2010.07186
101. The central sphere of an ALE space, Quart. J. Math. Oxford, 72 (2021) 253–276, arXiv:2008.05915
100. Integrable systems and Special Kähler metrics, EMS Surveys in Mathematical Sciences, 8 (2021) 163–178, arXiv:1910.05170
99. SL(2) over the octonions, Mathematical Proceedings of the Royal Irish Academy, 118A (2018) 21–38, arXiv:1805.02224
98. Critical loci for Higgs bundles, Comm. Math. Phys. 366 (2019), no. 2, 841–864, arXiv:1712.09928
97. Remarks on Nahm’s equations, in ''Modern Geometry: A celebration of the work of Simon Donaldson'' , V. Munoz et al. (eds.), Proceedings of Symposia in Pure Mathematics 99, American Math. Soc. (2018), 83–96, arXiv:1708.08812
96. Spinors, Lagrangians and rank 2 Higgs bundles, Proc. London Math. Soc. 115 (2017) 33–54, MR3669932, arXiv:1605.06385
95. Higgs bundles and diffeomorphism groups, in "Surveys in Differential Geometry Vol. 21", H.-D. Cao and S.-T. Yau (eds.), International Press, Cambridge, Mass. (2016), 139–163, MR3525096, arXiv:1501.04989
94. A note on vanishing theorems, in "Geometry and analysis on manifolds", in memory of Professor Shoshichi Kobayashi, T. Ochiai et al. (eds.), Progress in Mathematics 308 373–382 Birkhäuser (2015), MR3331406, arXiv:1408.0885
93. Manifolds with holonomy U*(2m), Revista Matemática Complutense 27 (2014), 351–368, MR3223571, arXiv:1403.7133
92. Higgs bundles and characteristic classes, in "Arbeitstagung Bonn 2013", in memory of Friedrich Hirzebruch, W. Ballmann et al. (eds.) Progress in Mathematics 319 247–264 Birkhäuser (2016), MR3618052, arXiv:1308:4603
91. (with L. Schaposnik) Nonabelianization of Higgs bundles, J. Differential Geometry 97 (2014), 79–89, MR3229050.
90. The hyperholomorphic line bundle, in "Algebraic and Complex Geometry", A. Frühbis-Krüger et al (eds), Springer Proceedings in Mathematics and Statistics 71 (2014) 209–223, arXiv:1306.4241
89. On the hyperkähler/quaternion Kähler correspondence, Communications in Mathematical Physics 324 (2013), No. 1, 77–106, MR3116317, arXiv:1210.0424
88. Deformations of holomorphic Poisson manifolds, Moscow Mathematical Journal 12 (2012), 567-591. arXiv:1105.4775
87. Generalized holomorphic bundles and the B-field action, Journal of Geometry and Physics 61 (2011), 352–362. arXiv:1010.0207
86. Lectures on generalized geometry, in "Surveys in Differential Geometry Vol. 16", N.-C. Leung and S.-T. Yau, (eds.), International Press, Cambridge, Mass. (2011), 79 – 124. arXiv:1008.0973
85. (with M.F. Atiyah and R. Dijkgraaf) Geometry and Physics, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 368 (2010) 913–926.
84. Stable bundles and polyvector fields, in "Complex and Differential Geometry", W. Ebeling et al (eds.) Springer Proceedings in Mathematics 8, 135–156, Springer Verlag, Heidelberg (2011). arXiv:1004.5313
83. The Atiyah-Singer index theorem, in "The Abel Prize: The first five years" (H. Holden and R. Piene eds.), 105 – 133, Springer Verlag, Heidelberg (2009).
82. Poisson modules and generalized geometry, in "Geometry and Analysis Vol. 1", Lizhen Ji (ed.) 403–406, Advanced Lectures in Mathematics 17, Higher Education Press Beijing (2010). arXiv:0905.3227
81. Vector bundles and the icosahedron, in "Vector bundles and complex geometry" O.Garcia- Prada et al (eds.) Contemporary Mathematics 522, 71 – 88, American Mathematical Society, Providence RI, (2010). arXiv:0906.4208
80. Einstein metrics and magnetic monopoles, in "Géométrie différentielle, physique mathématique, mathématiques et société (I)", (O. Hijazi, ed.) Astérisque 321 5–29 Société Mathématiques de France (2008).
79. Spherical harmonics and the icosahedron, in "Groups and symmetries", 215–231, CRM Proc. Lecture Notes 47 Amer. Math. Soc., Providence, RI, (2009). arXiv:0706.0088
78. Quaternionic Kähler moduli spaces, in "Riemannian Topology and Geometric Structures on Manifolds", K. Galicki and S.R. Simanca (eds.), Progress in Mathematics 271 49–61, Birkhäuser (2008).
77. Higgs bundles in the vector representation, in "Moduli spaces and vector bundles", S.Bradlow, L. Brambila-Paz, O.Garcia-Prada and S.Ramanan (eds.), London Mathematical Society Lecture Notes 359 473–483, Cambridge University Press, Cambridge (2009).
76. Interaction between mathematics and physics, ARBOR Ciencia, Pensamiento y Cultura, CLXXXIII 725 (2007).
75. Langlands duality and $G_2$ spectral curves, Quart. J. Math. Oxford. 58 (2007) 319–344, MR2354922, arXiv:math/0611524
74. Bihermitian metrics on Del Pezzo surfaces, Journal of Symplectic Geometry 5, (2007) 1–7. MR2371181 arXiv: math.DG/0608213
73. Generalized geometry — an introduction, to appear in "IRMA Lectures in Mathematics and Theoretical Physics", V.Cortes (ed.), European Mathematical Society.
72. Low dimensional geometry — a variational approach, (notes by M.Gualtieri), in ``Perspectives in Geometry", V.Apostolov, A.Dancer, N.Hitchin & M.Wang (eds.), CRM Proceedings and Lecture Notes, V. Volume 40, American Mathematical Society, Providence (2006).
71. Brackets, forms and invariant functionals, Asian J. Math 10 (2006) 541–560., MR2253158, arXiv: math.DG/0508618
70. Instantons, Poisson structures and generalized Kähler geometry, Commun. Math. Phys. 265 (2006) 131 – 317. MR2217300, arXiv:math.DG/0503432
69. Shiing-Shen Chern: 1911–2004, Bulletin of the London Math. Soc, 38 (2006) 507–519. MR2239046
68. Arthur Geoffrey Walker: 1909–2001, Biographical Memoirs of the Royal Society, (to appear)
67. Geometry in Oxford 1960–1990, in "Matematica e Cultura" Vol. 1, Giulio Einaudi Editore, Torino (to appear)
66. (with S. Cherkis), Gravitational instantons of type Dk , Comm. Math. Phys. 260 (2005), no. 2, 299–317. MR2177322, arXiv:hep-th/0310084.
65. What is a gerbe? Notices of the AMS, 50 No 2 (2003), 218 – 219.
64. A lecture on the octahedron, Bulletin of the London Math Soc, 35 (2003) 577–600. MR1989487
63. 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), MR2103721
62. Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford, 54 (2003) 281–308, MR2013140, arXiv:math.DG/0209099
61. 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). arXiv:math.DG/0107101
60. The geometry of three-forms in six dimensions, J. Differential Geometry 55 (2000), 547 - 576. arXiv:math.DG/0010054
59. The Wess-Zumino term for a harmonic map, Journal für die reine und angewandte Mathematik 543 (2002) 83 -101. arXiv:math.DG/0008038
58. Global Differential Geometry, in "Mathematics Unlimited - 2001 and Beyond", (B.Enquist and W.Schmid (Eds)), Springer Verlag, Heidelberg (2000) 577 - 591.
57. Sir Michael Atiyah: a brief biography in "The Founders of Index Theory", S-T Yau (ed.), International Press, Boston (2004)
56. L2-cohomology of hyperkähler quotients. Commun. Math. Phys. 211 (2000), 153 -165. MR1757010, arXiv:math.DG/9909002
55. (with J. Sawon) Curvature and characteristic numbers of hyperkähler manifolds, Duke Mathematical Journal 106 (2001), 599 - 615. MR1813238, arXiv:math.DG/9908114
54. 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. MR1876068, arXiv:math.DG/9907034
53. 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. MR1967750
52. (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). MR1723385
51. The moduli space of complex Lagrangian submanifolds, Asian Journal of Mathematics, 3 (1999) 77 - 92. MR1701923, arXiv:math.DG/9901069
50. 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. MR 1726926
49. 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. MR1634502
48. The moduli space of special Lagrangian submanifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997), no. 3 - 4, 503 - 515 MR1655530, arXiv:dg-ga/9711002
47. Geometrical aspects of Schlesinger's equation, Journal of Geometry and Physics 457 (1997), 1 - 14. MR1484592
46. Lectures on Frobenius manifolds, in "Gauge Theory and Symplectic Geometry'', J.Hurtubise & F.Lalonde (eds), NATO ASI Series C 488, Kluwer, Dordrecht (1997). MR1461570
45. Einstein metrics and the eta-invariant, Bollettino UMI (7) 11-B Suppl. fasc. 2 (1997), 95 - 105. MR1456253
44. 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. MR1397980
43. A new family of Einstein metrics, in " Manifolds and geometry (Pisa, 1993)'', 190 - 222, Sympos. Math., XXXVI, Cambridge Univ. Press, Cambridge, 1996. MR1410073
42. Poncelet polygons and the Painlevé equations, in "Geometry and analysis (Bombay, 1992)'', 151 - 85, Oxford University Press, Bombay, 1996. MR1351506
41. (with N.S. Manton and M.K. Murray) Symmetric monopoles, Nonlinearity 8 (1995), 661 - 692. MR1355037, arXiv:dg-ga/9503016
40. Twistor spaces, Einstein metrics and isomonodromic deformations, J. Differential Geom. 42 (1995), 30 - 112. MR1350695
39. Vector bundles in algebraic geometry, in "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 MR 96a:14003
38. Hyperkähler manifolds, Séminaire Bourbaki, Vol. 1991/92. Astérisque No. 206 (1992), Exp. No. 748, 3, 137-166. MR1206066
37. Lie groups and Teichmüller space, Topology 31 (1992), 449 - 473. MR1174252
36. 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. MR1182164
35. (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). MR1137269
34. Vector fields on the circle, in "Mechanics, analysis and geometry: 200 years after Lagrange'', North-Holland Delta Ser., North-Holland, Amsterdam, (1991), 359 - 378. MR1098524
33. 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. MR1171910
32. Hypersymplectic quotients, Atti della Accademia delle Scienze di Torino, Classe di Scienze Fisiche, Matematiche e Naturali, 124 Supp. (1990), 169 - 180.
31. 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. MR1084202
30. Flat connections and geometric quantization, Comm. Math. Phys. 131 (1990), 347-380. MR1065677
29. Harmonic maps from a 2-torus to the 3-sphere, J. Differential Geom. 31 (1990), 627-710. MR1053342
28. Gauge theory on Riemann surfaces, in "Lectures on Riemann surfaces (Trieste, 1987)'', 99-118, World Sci. Publishing, Teaneck, NJ, 1989. MR1082352
27. Harmonic maps from T2 to S3 , in "Harmonic mappings, twistors, and σ-models (Luminy, 1986)'', 103-112, Adv. Ser. Math. Phys., 4, World Sci. Publishing, Singapore, 1988. MR0982525
26. (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 MR0934202
25. "Monopoles, minimal surfaces, and algebraic curves.'' Séminaire de Mathématiques Supérieures, 105. Presses de l'Université de Montréal, Montreal, PQ, 1987. 94 pp. ISBN: 2-7606-0801-8 MR0935967
24. (with M.K. Murray) Spectral curves and the ADHM method, Comm. Math. Phys. 114 (1988), 463-474. MR0929140
23. The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), 59-126. MR0887284
22. Stable bundles and integrable systems, Duke Math. J. 54 (1987), 91–114, MR0885778
21. 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). MR0905894
20. (with A. Karlhede, U. Lindström, M. Rocek) Hyperkähler metrics and supersymmetry, Comm. Math. Phys. 108 (1987), 535-589. MR0877637
19. 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. MR0860411
18. (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. MR0836746
17. (with M.F. Atiyah) Low energy scattering of nonabelian monopoles, Phys. Lett. A 107 (1985), 21-25. MR0836746
16. The geometry of monopoles, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 541-547, PWN, Warsaw, 1984. MR0804710
15. Twistor construction of Einstein metrics, in "Global Riemannian geometry'' (Durham, 1983), 115-125, Ellis Horwood Ser.: Math. Appl., Horwood, Chichester, 1984. MR0757213
14. "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. MR0757199
13. 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). MR0728987
12. On the construction of monopoles, Commun. Math. Phys. 89 (1983) 145-190. MR0709461
11. Monopoles and geodesics, Commun. Math. Phys. 83 (1982) 579-602. MR0649818
10. 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). MR0699802
9. Kählerian twistor spaces, Proc. London Math. Soc. 43 (1981), 133-150. MR0623721
8. Linear field equations on self-dual spaces, Proc. Roy. Soc. London Ser. A 370 (1980), 173-191. MR0563832
7. (with M.F. Atiyah, V.G. Drinfeld, and Y.I. Manin) Construction of instantons, Phys. Lett. A 65 (1978), 185-187. MR0598562
6. Polygons and gravitons, Math. Proc. Camb. Phil. Soc. 85 (1979), 465-476. MR0520463
5. (with M.F. Atiyah and I.M. Singer) Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser A 362 (1978), 425-461. MR0506229
4. (with M.F. Atiyah and I.M. Singer) Deformations of instantons, Proc. Nat. Acad. Sci. USA (1977) 7, 2662-2663. MR0458424
3. On the curvature of rational surfaces, Proc. Sympos. Pure Math. XXVII, pp 65-80, Amer. Math. Soc. Providence RI (1975). MR0400127
2. Harmonic spinors, Advances in Mathematics 14 (1974), 1-55. MR0358873
1. Compact four-dimensional Einstein manifolds, J.Differential Geometry 9 (1974), 435-441. MR0350657