Publications of Nigel Hitchin


  1. Spectral curves and their impact, in “Crelle Bicentennial Edition”, C. Goldstein, D. Huybrechts and J. Schwermer (eds.), De Gruyter, Berlin (2026), 298–308.
  2. Ioan MacKenzie James, 1928–2025, Biogr. Mem. Fellows R. Soc. (2026).
  3. Ian Grant Macdonald, 1928–2023, Biogr. Mem. Fellows R. Soc. 79 (2026), 265–283.
  4. Gauge theory in pure mathematics, Bull. Amer. Math. Soc. (N.S.) (to appear), in memory of Jim Simons.
  5. A universal Higgs bundle moduli space, J. Geom. Phys. 229 (2026), Paper No. 105955, 9 pp. arXiv:2603.21712, MR5108292
  6. On the paper “Bundle gerbes” by Michael Murray, J. Lond. Math. Soc. (2) 113 (2026), no. 1, Paper No. e70374, 6 pp. MR5011580
  7. Remarks on the intersection of two quadrics, in “Algebraic geometry and the Langlands program”, Simons Symp., Springer (to appear), a volume in honour of Gérard Laumon. arXiv:2506.23671
  8. The Dirac operator, Bull. Amer. Math. Soc. (N.S.) 62 (2025), no. 1, 3–16. MR4845922
  9. Spinor-valued Higgs fields, in “Advances on complex Lagrangians, integrable systems and quantization”, L. Schaposnik (ed.), World Scientific Studies in Pure Mathematics 1, (to appear). arXiv:2404.12981
  10. Michael Atiyah: geometry and physics, in “Expanding Horizons of Mathematics”, Harv. Univ. Cent. Math. Sci. Appl. Ser. Math. 3, Int. Press, Somerville, MA (2024), 197–235. MR4950524
  11. ALE spaces and nodal curves, Q. J. Math. 76 (2025), no. 1, 337–347. arXiv:2402.04021, MR4865839
  12. (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. MR4454143
  13. A note on coupled Dirac operators, SIGMA Symmetry Integrability Geom. Methods Appl. 19 (2023), Paper No. 003, 9 pp. arXiv:2210.17512, MR4533558
  14. Multiplicity algebras for rank 2 bundles on curves of small genus, Internat. J. Math. 35 (2024), no. 9, Paper No. 2441011, 17 pp. arXiv:2203.03424, MR4772110
  15. A remark on calibrations and Lie groups, Pure Appl. Math. Q. 19 (2023), no. 6, 2663–2673. arXiv:2201.06331, MR4703029
  16. Spinors, twistors and classical geometry, SIGMA Symmetry Integrability Geom. Methods Appl. 17 (2021), Paper No. 090, 9 pp. arXiv:2108.02603, MR4322108
  17. (with T. Hausel) Very stable Higgs bundles, equivariant multiplicity and mirror symmetry, Invent. Math. 228 (2022), no. 2, 893–989. arXiv:2101.08583, MR4411733
  18. A Teichmüller space for negatively curved surfaces, Proc. Lond. Math. Soc. (3) 126 (2023), no. 3, 900–922. arXiv:2010.07186, MR4563863
  19. The central sphere of an ALE space, Q. J. Math. 72 (2021), no. 1-2, 253–276. arXiv:2008.05915, MR4271387
  20. Integrable systems and Special Kähler metrics, EMS Surv. Math. Sci. 8 (2021), no. 1-2, 163–178. arXiv:1910.05170, MR4307206
  21. Sir Michael Atiyah OM 1929–2019, Biogr. Mem. Fellows R. Soc. 69 (2020), 9–35.
  22. SL(2) over the octonions, Math. Proc. R. Ir. Acad. 118A (2018), no. 1, 21–38. arXiv:1805.02224, MR3811489
  23. Critical loci for Higgs bundles, Comm. Math. Phys. 366 (2019), no. 2, 841–864. arXiv:1712.09928, MR3922539
  24. Remarks on Nahm’s equations, in “Modern geometry: a celebration of the work of Simon Donaldson”, V. Munoz et al. (eds.), Proc. Sympos. Pure Math. 99, Amer. Math. Soc., Providence, RI (2018), 83–95. arXiv:1708.08812, MR3838880
  25. Spinors, Lagrangians and rank 2 Higgs bundles, Proc. Lond. Math. Soc. (3) 115 (2017), no. 1, 33–54. arXiv:1605.06385, MR3669932
  26. Higgs bundles and diffeomorphism groups, in “Surveys in differential geometry 2016. Advances in geometry and mathematical physics”, H.-D. Cao and S.-T. Yau (eds.), Surv. Differ. Geom. 21, Int. Press, Somerville, MA (2016), 139–163. arXiv:1501.04989, MR3525096
  27. A note on vanishing theorems, in “Geometry and analysis on manifolds”, T. Ochiai et al. (eds.), Progr. Math. 308, Birkhäuser/Springer, Cham (2015), 373–382, in memory of Professor Shoshichi Kobayashi. arXiv:1408.0885, MR3331406
  28. Manifolds with holonomy U∗(2m), Rev. Mat. Complut. 27 (2014), no. 2, 351–368. arXiv:1403.7133, MR3223571
  29. Higgs bundles and characteristic classes, in “Arbeitstagung Bonn 2013”, W. Ballmann et al. (eds.), Progr. Math. 319, Birkhäuser/Springer, Cham (2016), 247–264, in memory of Friedrich Hirzebruch. arXiv:1308.4603, MR3618052
  30. (with L. Schaposnik) Nonabelianization of Higgs bundles, J. Differential Geom. 97 (2014), no. 1, 79–89. arXiv:1307.0960, MR3229050
  31. The hyperholomorphic line bundle, in “Algebraic and complex geometry”, A. Frühbis-Krüger et al. (eds.), Springer Proc. Math. Stat. 71, Springer, Cham (2014), 209–223. arXiv:1306.4241, MR3278575
  32. On the hyperkähler/quaternion Kähler correspondence, Comm. Math. Phys. 324 (2013), no. 1, 77–106. arXiv:1210.0424, MR3116317
  33. Deformations of holomorphic Poisson manifolds, Mosc. Math. J. 12 (2012), no. 3, 567–591. arXiv:1105.4775, MR3024823
  34. Generalized holomorphic bundles and the B-field action, J. Geom. Phys. 61 (2011), no. 1, 352–362. arXiv:1010.0207, MR2747007
  35. Lectures on generalized geometry, in “Surveys in differential geometry. Volume XVI. Geometry of special holonomy and related topics”, N.-C. Leung and S.-T. Yau (eds.), Surv. Differ. Geom. 16, Int. Press, Somerville, MA (2011), 79–124. arXiv:1008.0973, MR2893677
  36. (with M. F. Atiyah and R. Dijkgraaf) Geometry and Physics, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 368 (2010), no. 1914, 913–926. MR2587923
  37. Stable bundles and polyvector fields, in “Complex and differential geometry”, W. Ebeling et al. (eds.), Springer Proc. Math. 8, Springer, Heidelberg (2011), 135–156. arXiv:1004.5313, MR2964473
  38. The Atiyah-Singer index theorem, in “The Abel Prize: The first five years”, H. Holden and R. Piene (eds.), Springer, Berlin (2009), 117–152.
  39. Poisson modules and generalized geometry, in “Geometry and analysis. No. 1”, Lizhen Ji (ed.), Adv. Lect. Math. (ALM) 17, Int. Press, Somerville, MA (2011), 403–417. arXiv:0905.3227, MR2882431
  40. Vector bundles and the icosahedron, in “Vector bundles and complex geometry”, O. Garcia-Prada et al. (eds.), Contemp. Math. 522, Amer. Math. Soc., Providence, RI (2010), 71–87. arXiv:0906.4208, MR2681722
  41. Einstein metrics and magnetic monopoles, in “Géométrie différentielle, physique mathématique, mathématiques et société (I)”, O. Hijazi (ed.), Astérisque 321, Soc. Math. France, Paris (2008), 5–29. MR2521642
  42. Spherical harmonics and the icosahedron, in “Groups and symmetries”, CRM Proc. Lecture Notes 47, Amer. Math. Soc., Providence, RI (2009), 215–231. arXiv:0706.0088, MR2500563
  43. Quaternionic Kähler moduli spaces, in “Riemannian topology and geometric structures on manifolds”, K. Galicki and S. R. Simanca (eds.), Progr. Math. 271, Birkhäuser Boston, Boston, MA (2009), 49–61. MR2494168
  44. 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 Math. Soc. Lecture Note Ser. 359, Cambridge Univ. Press, Cambridge (2009), 473–483. MR2537079
  45. Interaction between mathematics and physics, Arbor 183 (2007), no. 725, 427–432.
  46. Langlands duality and G2 spectral curves, Q. J. Math. 58 (2007), no. 3, 319–344. arXiv:math/0611524, MR2354922
  47. Bihermitian metrics on Del Pezzo surfaces, J. Symplectic Geom. 5 (2007), no. 1, 1–8. arXiv:math/0608213, MR2371181
  48. Generalized geometry — an introduction, in “Handbook of pseudo-Riemannian geometry and supersymmetry”, V. Cortés (ed.), IRMA Lect. Math. Theor. Phys. 16, Eur. Math. Soc., Zürich (2010), 185–208. MR2681591
  49. Low dimensional geometry — a variational approach, in “Perspectives in Riemannian geometry”, V. Apostolov, A. Dancer, N. Hitchin and M. Wang (eds.), CRM Proc. Lecture Notes 40, Amer. Math. Soc., Providence, RI (2006), 183–207, notes by M. Gualtieri. MR2237110
  50. Brackets, forms and invariant functionals, Asian J. Math. 10 (2006), no. 3, 541–560. arXiv:math/0508618, MR2253158
  51. Instantons, Poisson structures and generalized Kähler geometry, Comm. Math. Phys. 265 (2006), no. 1, 131–164. arXiv:math/0503432, MR2217300
  52. Shiing-Shen Chern: 1911–2004, Bull. London Math. Soc. 38 (2006), no. 3, 507–519. MR2239046
  53. Arthur Geoffrey Walker: 1909–2001, Biogr. Mem. Fellows R. Soc. 52 (2006), 413–421.
  54. La geometria a Oxford 1960–1990, in “La matematica, Vol. 1: I luoghi e i tempi”, C. Bartocci and P. Odifreddi (eds.), Giulio Einaudi Editore, Torino (2007), 711–734, English version: Mathematics and culture: geometry in Oxford 1960–1990, Celebratio Mathematica (2012).
  55. (with S. Cherkis) Gravitational instantons of type Dk, Comm. Math. Phys. 260 (2005), no. 2, 299–317. arXiv:hep-th/0310084, MR2177322
  56. What is a gerbe?, Notices Amer. Math. Soc. 50 (2003), no. 2, 218–219.
  57. A lecture on the octahedron, Bull. London Math. Soc. 35 (2003), no. 5, 577–600. MR1989487
  58. Special holonomy and beyond, in “Strings and geometry”, M. Douglas, J. Gauntlett and M. Gross (eds.), Clay Math. Proc. 3, Amer. Math. Soc., Providence, RI (2004), 159–175. MR2103721
  59. Generalized Calabi-Yau manifolds, Q. J. Math. 54 (2003), no. 3, 281–308. arXiv:math/0209099, MR2013140
  60. Stable forms and special metrics, in “Global differential geometry: the mathematical legacy of Alfred Gray (Bilbao, 2000)”, M. Fernández and J. A. Wolf (eds.), Contemp. Math. 288, Amer. Math. Soc., Providence, RI (2001), 70–89. arXiv:math/0107101, MR1871001
  61. The geometry of three-forms in six dimensions, J. Differential Geom. 55 (2000), no. 3, 547–576. arXiv:math/0010054, MR1863733, Project Euclid
  62. The Wess-Zumino term for a harmonic map, J. Reine Angew. Math. 543 (2002), 83–101. arXiv:math/0008038, MR1887879
  63. Global Differential Geometry, in “Mathematics unlimited—2001 and beyond”, B. Engquist and W. Schmid (eds.), Springer, Berlin (2001), 577–591. MR1852178
  64. Sir Michael Atiyah: a brief biography, in “The Founders of Index Theory”, S.-T. Yau (ed.), Int. Press, Boston (2004).
  65. L2-cohomology of hyperkähler quotients, Comm. Math. Phys. 211 (2000), no. 1, 153–165. arXiv:math/9909002, MR1757010
  66. (with J. Sawon) Curvature and characteristic numbers of hyperkähler manifolds, Duke Math. J. 106 (2001), no. 3, 599–615. arXiv:math/9908114, MR1813238
  67. Lectures on special Lagrangian submanifolds, in “Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999)”, Cumrun Vafa and S.-T. Yau (eds.), AMS/IP Stud. Adv. Math. 23, Amer. Math. Soc., Providence, RI (2001), 151–182. arXiv:math/9907034, MR1876068
  68. The Dirac operator, in “Invitations to geometry and topology”, M. Bridson and S. Salamon (eds.), Oxf. Grad. Texts Math. 7, Oxford Univ. Press, Oxford (2002), 208–232. MR1967750
  69. (with G. B. Segal and R. S. Ward) Integrable systems: Twistors, loop groups and Riemann surfaces, Oxf. Grad. Texts Math. 4, Oxford Univ. Press, Oxford (1999). MR1723385
  70. The moduli space of complex Lagrangian submanifolds, Asian J. Math. 3 (1999), no. 1, 77–91, special issue “Sir Michael Atiyah: a great mathematician of the twentieth century”. arXiv:math/9901069, MR1701923
  71. Integrable systems in Riemannian geometry, in “Surveys in differential geometry: integral systems [integrable systems]”, C.-L. Terng and K. Uhlenbeck (eds.), Surv. Differ. Geom. 4, Int. Press, Boston, MA (1998), 21–81. MR1726926
  72. 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 Univ. Press, Oxford (1998), 9–30. MR1634502
  73. The moduli space of special Lagrangian submanifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997), no. 3-4, 503–515, dedicated to Ennio De Giorgi. arXiv:dg-ga/9711002, MR1655530
  74. Geometrical aspects of Schlesinger’s equation, J. Geom. Phys. 23 (1997), no. 3-4, 287–300. MR1484592
  75. Lectures on Frobenius manifolds, in “Gauge theory and symplectic geometry (Montreal, PQ, 1995)”, J. Hurtubise and F. Lalonde (eds.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 488, Kluwer Acad. Publ., Dordrecht (1997), 69–112. MR1461570
  76. Einstein metrics and the eta-invariant, Boll. Un. Mat. Ital. B (7) 11 (1997), no. 2, suppl., 95–105. MR1456253
  77. Magnetic monopoles with Platonic symmetry, in “Moduli of vector bundles (Sanda, 1994; Kyoto, 1994)”, Lecture Notes in Pure and Appl. Math. 179, Dekker, New York (1996), 55–63. MR1397980
  78. A new family of Einstein metrics, in “Manifolds and geometry (Pisa, 1993)”, Sympos. Math., XXXVI, Cambridge Univ. Press, Cambridge (1996), 190–222. MR1410073
  79. Poncelet polygons and the Painlevé equations, in “Geometry and analysis (Bombay, 1992)”, Tata Inst. Fund. Res., Bombay (1995), 151–185. MR1351506
  80. (with N. S. Manton and M. K. Murray) Symmetric monopoles, Nonlinearity 8 (1995), no. 5, 661–692. arXiv:dg-ga/9503016, MR1355037, IOP
  81. Twistor spaces, Einstein metrics and isomonodromic deformations, J. Differential Geom. 42 (1995), no. 1, 30–112. MR1350695, Project Euclid
  82. Vector bundles in algebraic geometry, N. J. Hitchin, P. E. Newstead and W. M. Oxbury (eds.), London Math. Soc. Lecture Note Ser. 208, Cambridge Univ. Press, Cambridge (1995), Proceedings of the symposium held in Durham, 1993. 345 pp. ISBN: 0-521-49878-3. MR 96a:14003
  83. Hyperkähler manifolds, in “Séminaire Bourbaki, Vol. 1991/92”, Astérisque 206, (1992), Exp. No. 748, 137–166. MR1206066
  84. Lie groups and Teichmüller space, Topology 31 (1992), no. 3, 449–473. MR1174252
  85. The symplectic geometry of moduli spaces of connections and geometric quantization, Progr. Theoret. Phys. Suppl. 102 (1991), 159–174, in “Common trends in mathematics and quantum field theories (Kyoto, 1990)”. MR1182164
  86. (with M. F. Atiyah) Geometriya i dinamika magnitnykh monopolei, Mir, Moscow (1991), (Russian) [The geometry and dynamics of magnetic monopoles] Translated from the English and with a preface by O. V. Ogievetskii. MR1137269
  87. 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
  88. 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
  89. Hypersymplectic quotients, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 124 (1990), no. suppl., 169–180.
  90. 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
  91. Flat connections and geometric quantization, Comm. Math. Phys. 131 (1990), no. 2, 347–380. MR1065677, Project Euclid
  92. Harmonic maps from a 2-torus to the 3-sphere, J. Differential Geom. 31 (1990), no. 3, 627–710. MR1053342
  93. Gauge theory on Riemann surfaces, in “Lectures on Riemann surfaces (Trieste, 1987)”, World Sci. Publ., Teaneck, NJ (1989), 99–118. MR1082352
  94. Harmonic maps from T2 to S3, in “Harmonic mappings, twistors, and σ-models (Luminy, 1986)”, Adv. Ser. Math. Phys. 4, World Sci. Publishing, Singapore (1988), 103–112. MR0982525
  95. (with M. F. Atiyah) The geometry and dynamics of magnetic monopoles, M. B. Porter Lectures, Princeton Univ. Press, Princeton, NJ (1988), viii+134 pp. ISBN: 0-691-08480-7. MR0934202
  96. Monopoles, minimal surfaces, and algebraic curves, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics] 105, Presses de l’Université de Montréal, Montreal, QC (1987), 94 pp. ISBN: 2-7606-0801-8. MR0935967
  97. (with M. K. Murray) Spectral curves and the ADHM method, Comm. Math. Phys. 114 (1988), no. 3, 463–474. MR0929140, Project Euclid
  98. The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), no. 1, 59–126. MR0887284
  99. Stable bundles and integrable systems, Duke Math. J. 54 (1987), no. 1, 91–114. MR0885778
  100. Monopole and vortex scattering, in “Field theory, quantum gravity and strings, II (Meudon/Paris, 1985/1986)”, Lecture Notes in Phys. 280, Springer, Berlin (1987), 117–124. MR0905894
  101. (with A. Karlhede, U. Lindström, M. Roček) Hyperkähler metrics and supersymmetry, Comm. Math. Phys. 108 (1987), no. 4, 535–589. MR0877637, Project Euclid
  102. Metrics on moduli spaces, in “The Lefschetz centennial conference, Part I (Mexico City, 1984)”, Contemp. Math. 58, Amer. Math. Soc., Providence, RI (1986), 157–178. MR0860411
  103. (with M. F. Atiyah) Low-energy scattering of nonabelian magnetic monopoles, Philos. Trans. Roy. Soc. London Ser. A 315 (1985), no. 1533, 459–469, in “New developments in the theory and application of solitons. With discussion.”. MR0836746
  104. (with M. F. Atiyah) Low energy scattering of nonabelian monopoles, Phys. Lett. A 107 (1985), no. 1, 21–25. MR0778313
  105. The geometry of monopoles, in “Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983)”, PWN, Warsaw (1984), 541–547. MR0804710
  106. Twistor construction of Einstein metrics, in “Global Riemannian geometry (Durham, 1983)”, Ellis Horwood Ser. Math. Appl., Horwood, Chichester (1984), 115–125. MR0757213
  107. Global Riemannian geometry, T. J. Willmore and N. J. Hitchin (eds.), Ellis Horwood Ser. Math. Appl., Ellis Horwood; Halsted Press [John Wiley & Sons], Chichester; New York (1984), Proceedings of the symposium held at the University of Durham, Durham, July 1983. MR0757199
  108. The Yang-Mills equations and the topology of 4-manifolds (after Simon Donaldson), in “Bourbaki seminar, Vol. 1982/83”, Astérisque 105-106, Soc. Math. France, Paris (1983), 167–178. MR0728987
  109. On the construction of monopoles, Comm. Math. Phys. 89 (1983), no. 2, 145–190. MR0709461, Project Euclid
  110. Monopoles and geodesics, Comm. Math. Phys. 83 (1982), no. 4, 579–602. MR0649818, Project Euclid
  111. Complex manifolds and Einstein’s equations, in “Twistor geometry and nonlinear systems (Primorsko, 1980)”, H. Doebner et al. (eds.), Lecture Notes in Math. 970, Springer, Berlin-New York (1982), 73–99. MR0699802
  112. Kählerian twistor spaces, Proc. London Math. Soc. (3) 43 (1981), no. 1, 133–150. MR0623721
  113. Linear field equations on self-dual spaces, Proc. Roy. Soc. London Ser. A 370 (1980), no. 1741, 173–191. MR0563832
  114. (with M. F. Atiyah, V. G. Drinfeld, and Y. I. Manin) Construction of instantons, Phys. Lett. A 65 (1978), no. 3, 185–187. MR0598562
  115. Polygons and gravitons, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 3, 465–476. MR0520463
  116. (with M. F. Atiyah and I. M. Singer) Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978), no. 1711, 425–461. MR0506229
  117. (with M. F. Atiyah and I. M. Singer) Deformations of instantons, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 7, 2662–2663. MR0458424, PNAS
  118. On the curvature of rational surfaces, in “Differential geometry (Stanford Univ., Stanford, Calif., 1973)”, Proc. Sympos. Pure Math., Vol. XXVII, Part 2, Amer. Math. Soc., Providence, RI (1975), 65–80. MR0400127
  119. Harmonic spinors, Advances in Math. 14 (1974), 1–55. MR0358873
  120. Compact four-dimensional Einstein manifolds, J. Differential Geom. 9 (1974), 435–441. MR0350657