Oscar García-Prada

Profesor de Investigación, CSIC





List of publications in pdf file

Articles

  1. (with M. del Olmo, M. Santander), Locally operating realizations of non-connected transformation Lie groups, J. Math. Phys. 29 (1988) 1083-1090.
  2. Invariant connections and vortices, Communications in Mathematical Physics 156 (1993) 527-546.
  3. A direct existence proof for the vortex equations over a compact Riemann surface, Bull. London Math. Soc. 26 (1994) 88-96.
  4. Dimensional reduction of stable bundles, vortices and stable pairs, Interna. J. Math., 5 (1994) 1-52.
  5. Vortices on Riemann surfaces, Seminari di Geometria 1994-95, University of Bologna, 141-152.
  6. (with S. Bradlow), Stable triples, equivariant bundles and dimensional reduction, Math. Ann. 304 (1996) 225-252.
  7. (with S. Bradlow, G. Daskalopoulos, R. Wentworth), Stable augmented bundles over Riemann surfaces, in Vector Bundles in Algebraic Geometry (Durham 1993), edited by N.J. Hitchin, P.E. Newstead and W.M. Oxbury, London Math. Soc. Lecture Notes Series, 208 (1995) 15-68 Cambridge University Press.
  8. (with S. Bradlow), Higher cohomology triples and holomorphic extensions, Comm. in Analysis and Geom. 3 (1995) 421-464.
  9. The Seiberg-Witten invariants and the vortex equations, Differential Geometry and its Applications, Santiago de Compostela 1995, eds. M. Salgado, E. Vázquez, Anales de Física, Monografías 3 (1996) 167-181.
  10. (with S. Bradlow), Non-abelian monopoles and vortices, Geometry and Physics (Aarhus 1995), eds. J. Andersen, J. Dupont, H. Pedersen, A. Swann, Marcel Dekker (1996) 567-589.
  11. (with O. Biquard), Parabolic vortex equations and instantons of infinite energy, J. Geom. and Phys. 21 (1997) 238-254.
  12. Seiberg-Witten invariants and vortex equations, Quantum Symmetries, eds. A. Connes, K. Gawedzki, J. Zinn-Justin, Elsevier (1998) 886-934.
  13. (with S. Bradlow), A Hitchin-Kobayashi correspondence for coherent systems on Riemann surfaces, J. London Math. Soc. (2) 60 (1999) 155-170.
  14. Entrevista a Roger Penrose, Gaceta de la Real Sociedad Matemática Española, 21 (1999).
  15. Entrevista a Roger Penrose, Revista de Cultura Lateral, Año VI 54 (1999).
  16. (with S. Ramanan), Twisted Higgs bundles and the fundamental group of compact Kähler manifolds, Mathematical Research Letters, 7, 1-18 (2000).
  17. Interview with Roger Penrose (I), Newsletter of the European Mathematical Society, 38 (2000) 17-21.
  18. Interview with Roger Penrose (II), Newsletter of the European Mathematical Society, 39 (2001) 12-17.
  19. (with L. Alvarez-Cónsul), Dimensional reduction, SL(2,C)-equivariant bundles and stable holomorphic chains, Interna. J. Math., 12 (2001) 159-201.
  20. (with S. Bradlow, P.B. Gothen), Representations of the fundamental group of a surface in PU(p,q) and holomorphic triples, C.R. Acad. Sci. Paris, t. 333, série I (2001) 347-352.
  21. (with L. Alvarez-Cónsul), Dimensional reduction, Hitchin-Kobayashi correspondence for equivariant bundles on XxP1, Global Differential Geometry: The Mathematical Legacy of Alfred Gray, Contemporary Mathematics, 288 (2001) 249-257.
  22. (with J.P. Bourguignon, E. Calabi, J. Eells, M. Gromov), Where does geometry go? A research and education perspective, Global Differential Geometry: The Mathematical Legacy of Alfred Gray, Contemporary Mathematics, 288 (2001) 442-457.
  23. (with S. Bradlow),An application of coherent systems to a Brill-Noether problem, J. reine angew. Math 551 (2002) 123-143.
  24. (with L. Álvarez-Cónsul), Dimensional reduction and quiver bundles, J. reine angew. Math., 556 (2003) 1-46.
  25. (with L. Álvarez-Cónsul), Hitchin-Kobayashi correspondence, quivers and vortices, Comm. Math. Phys., 238 (2003) 1-33.
  26. (with S. Bradlow and I. Mundet i Riera), Relative Hitchin-Kobayashi correspondence for principal pairs, Quarterly Journal of Mathematics, 54 (2003) 111-170.
  27. (with S. Bradlow, V. Muñoz y P.E. Newstead), Coherent systems and Brill-Noether theory, Interna. J. Math. 14 (2003) 683-733.
  28. (with S. Bradlow, y P.B. Gothen), Surface group representations and U(p,q)-Higgs bundles, J. Differential Geometry, 64 (2003) 111-170.
  29. (with S. Bradlow and P.B. Gothen), Moduli spaces of holomorphic triples over compact Riemann surfaces, Math. Ann., 328 (2004) 299-351.
  30. (with S. Bradlow and P.B. Gothen), Representations of surface groups in the general linear group, Publicaciones de la RSME, 7 (2004) 83-94.
  31. (with I. Mundet i Riera), Representations of the fundamental group of a closed oriented surface in Sp(4,R), Topology 43 (2004) 831-855.
  32. El teorema del índice de Atiyah-Singer, EL PAÍS, 26 de mayo de 2004, p. 35.
  33. (with D. Hernández Ruipérez, F. Pioli, and C. Tejero Prieto), Fourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves, J. Geom. and Phys., 55 (2005) 353-384.
  34. Matemáticas y Física Teórica, Matemáticas en la Comunidad de Madrid: Computación e Interacción I+D+i.
  35. Mathematical Physics, Bulletin ICM2006.
  36. (with P.B. Gothen, and V. Muñoz), Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, Memoirs of the American Mathematical Society, 187, No. 879 (2007).
  37. (with S. Bradlow and P.B. Gothen), Homotopy groups of moduli spaces of representations, Topology, 47 (2008), 203-224.
  38. (with S. Bradlow and P.B. Gothen), Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces, Geometriae Dedicata, 122 (2006) 185-213.
  39. (with L. Álvarez-Cónsul and A.H.W. Schmitt), On the geometry of moduli spaces of holomorphic chains over compact Riemann surfaces, International Mathematics Research Papers, (2006) 1-82.
  40. (with S. Bradlow, V. Mercat, V. Muñoz, and P.E. Newstead), On the geometry of moduli spaces of coherent systems on algebraic curves, Interna. J. Math., 18 (2007) 411-453.
  41. (with S. Bradlow and P. B. Gothen), What is a Higgs bundle?, Notices of the American Mathematical Society, 54, No. 8, (2007) 980-981.
  42. (with I. Biswas), A Higgs bundle on a Hermitian symmetric space, Geom. Dedicata, 127 (2007) 87-98.
  43. Involutions of the moduli space of SL(n,C)-Higgs bundles and real forms. In Vector Bundles and Low Codimensional Subvarieties: State of the Art and Recent Developments Quaderni di Matematica, Editors: G. Casnati, F. Catanese and R. Notari, 2007.
  44. (with M. Logares, and V. Muñoz), Connected components of the moduli space of parabolic U(p,q)-Higgs bundles, Quarterly Journal of Mathematics, Quart. J. Math. 00 (2008) 1–51; doi:10.1093/qmath/han001.
  45. Higgs bundles and surface group representations, in Moduli Spaces and Vector Bundles, LMS Lecture Notes Series, 359 (2009) 265-310.
  46. (with S. Bradlow, V. Mercat, V. Muñoz and P.E. Newstead), Moduli spaces of coherent systems of small slope on algebraic curves, Journal of Algebra, in press.
  47. (with I. Biswas), A Higgs bundle on a Hermitian symmetric space II, Geometriae Dedicata, 147 (2010) 187-190.
  48. (with D. Toledo), A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space, Geometry and Topology, 15:2 (2011) 1013-1027.
  49. Existencia de Yang Mills y del salto de masa, Jornadas RSME 2011, Los Problemas del Milenio, Edición PPU, (2011).
  50. (with A. Oliveira), Higgs bundles for the non-compact dual of the unitary group, Illinois Journal of Mathematics, 55 No. 3 (2011), 1155-1181.
  51. (with M. Aparicio Arroyo), Higgs bundles for the Lorentz group, Illinois Journal of Mathematics, 55 (2011) 1299-1326.
  52. (with S. Bradlow and P.B. Gothen), Deformations of maximal representations in Sp(4,R), Quarterly Journal of Mathematics, 63(4) (2012) 795-843.
  53. (with P.B. Gothen and I. Mundet i Riera), Higgs bundles and surface group representations in the real symplectic group, Journal of Topology, 6(1) (2013) 64-118.
  54. (with L. Álvarez-Cónsul and M. García-Fernández), Coupled equations for Kähler metrics and Yang-Mills connections, Geometry and Topology, 17 (2013) 2731-2812.
  55. (with J. Heinloth), The y-genus of the moduli space of PGLn-Higgs bundles on a curve (for degree coprime to n), Duke Mathematical Journal, 14 (2013) 2731-2749.
  56. (with J. Heinloth and A. Schmitt), On the motives of moduli of chains and Higgs bundles, Journal of the European Mathematical Society/, 16 (2014) 2617–2668.
  57. (with E. Franco and P.E. Newstead), Higgs bundles over elliptic curves, Illinois Journal of Mathematics, 58 (2014) 43–96..
  58. (with A. Oliveira), Connectedness of the moduli of Sp(2p; 2q)-Higgs bundles, Quarterly Journal of Mathematics, 65 (2014) 931–956.
  59. (with I. Biswas and J. Hurtubise), Pseudo-real principal Higgs bundles on compact Kaehler manifolds, Annales de l'Institut Fourier, 64 (2014)
  60. (with I. Biswas), Anti-holomorphic involutions of the moduli spaces of Higgs bundles, Journal de L’Ecole Polytechnique-Mathématiques, 2 (2014) 35–54.
  61. (with S. Bradlow and P.B. Gothen), Higgs bundles for the non-compact dual of the special orthogonal group, Geometriae Dedicata, 175 (2015) 1–48.
  62. (with I. Biswas and J. Hurtubise), Pseudo-real principal G-bundles over a real curve, Annales de l’Institut Fourier, 64 (2014) 2527–2562.
  63. Entrevista a Sir Michael Atiyah, La Gaceta de la RSME, 19 (2016) 275–291.
  64. Interview with Sir Michael Atiyah, EMS Newsletter, 102 (2016) 22–30.
  65. (with L. Alvarez-Cónsul and I. Biswas), A Tannakian approach to dimensional reduction of principal bundles, Journal of Geometry and Physics, 18 (2017) 4–19.
  66. (with L. Alvarez-Cónsul and M. Garcıa-Fernandez), Gravitating vortices, cosmic strings and the Kähler–Yang–Mills equations, Communications in Mathematical Physics, 351 (2017) 361–385.
  67. (with O. Biquard and R. Rubio), Higgs bundles, Toledo invariant and the Cayley correspondence, Journal of Topology, 10 (2017) 795–826.
  68. (with A. Oliveira), Maximal Higgs bundles for adjoint forms via Cayley correspondence, Geometriae Dedicata, 190 (2017) 1–22.
  69. (with A. Oliveira), Connectedness of the moduli of Higgs bundles, Asian Journal of Mathematics, 21 (2017) 791–810.
  70. (with A. Peón-Nieto and S. Ramanan), Higgs bundles for real groups and the Hitchin–Kostant–Rallis section, Transactions of the AMS, 370 (2018) 2907–2953.
  71. (with M. Aparicio-Arroyo, S.B. Bradlow, B. Collier, P.B. Gothen and A. Oliveira), Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars, Comptes Rendus Mathématiques, 356 (2018) 666–673.
  72. (with S. Ramanan), Involutions of rank 2 Higgs bundle moduli spaces Geometry and Physics: A Festschrift in honour of Nigel Hitchin, Oxford University Press, 2018.
  73. (with S.B. Bradlow, P. Gothen and J. Heinloth), Irreducibility of moduli of semistable Chains and applications to U(p,q)-Higgs bundles, Geometry and Physics: A Festschrift in honour of Nigel Hitchin, Oxford University Press, Oxford University Press, 2018.
  74. (with E. Franco and P.E. Newstead), Higgs bundles over elliptic curves for reductive groups, Glasgow Mathematical Journal, 61 (2019) 297–320.
  75. (with E. Franco and P.E. Newstead), Higgs bundles over elliptic curves for real groups, Quarterly Journal of Mathematics, 70 (2019) 105146.
  76. (with I. Biswas and J. Hurtubise), Branes and Langlands duality, Communications in Mathematical Physics, 365 (2019) 1005–1018.
  77. Sir Michael Atiyah, La Gaceta de la RSME, 22 Núm. 1 (2019) 171–187.
  78. Muere Michael Atiyah, uno de los mas grandes matematicos de nuestro tiempo, El País, 18 de enero de 2019.
  79. (with M. Aparicio-Arroyo, S.B. Bradlow, B. Collier, P.B. Gothen and A. Oliveira) SO(p,q)-Higgs bundles and higher Teichmüller components, Invent. Math., 218 (2019) 197–299.
  80. (with I. Biswas, L. A. Calvo, and E. Franco), Involutions of the moduli spaces of G-Higgs bundles over elliptic curves, J. Geometry and Physics, 142 (2019) 47–65.
  81. (with L. Alvarez-Cónsul, M. García-Fernández), On the Kähler–Yang–Mills–Higgs equations, Pure and Applied Mathematics Quarterly 15 (2019) 1181–1217.
  82. Higgs bundles and higher Teichmüller spaces, Handbook on Teichmüller theory Athanase Papadopoulos (editor), European Mathematical Society, 2020.
  83. (with I. Biswas, J. Hurtubise and S. Rayan), Principal co-Higgs bundles on P1, Proceedings of the Edinburgh Mathematical Society 63 (2020) 512–530.
  84. (with L. Alvarez-Cónsul, M. García-Fernández and V.P. Pingali), Gravitating vortices and Einstein-Bogomol'nyi equations, Mathematische Annalen (2020) https://doi.org/10.1007/s00208-020-01964-z.
  85. (with O. Biquard and I. Mundet i Riera), Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group, Advances in Mathematics, 372 (2020) 107305.
  86. (with D.A. Salamon and S. Trautwein), Complex structures, moment maps and the Ricci form, Asian Journal of Mathematics, to appear.
  87. (with D.A. Salamon), A moment map interpretation of the Ricci form, Kähler-Einstein structures, and Teichmüller spaces, Volume in honour of Boris Dubrovin, to appear.
  88. (with G. Wilkin), Action of the mapping class group on character varieties and Higgs bundles, Documenta Mathematica, to appear.

Preprints (arXiv)

  1. (with P.B. Gothen and I. Mundet i Riera), The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations, preprint arXiv:0909.4487.
  2. (with A. Peón-Nieto), Higgs bundles, abelian gerbs and cameral data, (arXiv:1902.06139).
  3. (with I. Biswas, and L. A. Calvo), Real Higgs pairs and non-abelian Hodge correspondence on a Klein surface, (arXiv:1904.10878).

Books

  1. Moduli spaces and geometric structures, appendix to the third edition of the book by R.O. Wells, Differential Analysis on Complex Manifolds, Springer, GTM 65, 2007.
  2. (with S. Bradlow, L. Brambila-Paz, S. Ramanan, editors), Moduli Spaces and Vector Bundles, LMS Lecture Notes Series 359, Cambridge University Press, 2009.
  3. (with D. Avritzer, L. Ein, E. Esteves, X. Gómez-Mont), Proceedings of the IV Iberoamerican Conference on Complex Geometry, Geometriae Dedicata, Springer, 139, 2009.
  4. (with J-P Bourguignon and S. Salamon, editors), The Many Facets of Geometry: A tribute to Nigel Hitchin, Oxford University Press, 2010.
  5. (with L. Álvarez-Cónsul, I. Biswas, S. B. Bradlow, T. Gómez and P.E. Newstead, editors), Vector Bundles and Complex Geometry, Proceedings of Conference on Vector Bundles in Honour of S. Ramanan, American Mathematical Society, 2010.
  6. (with V. Ginzburg, W. Goldman, V. E. Miranda, V. Muñoz, editors), Proceedings of GESTA Conference, Special volume, Geometriae Dedicata (Springer), Vol. 165 (1), 2013.
  7. (with L. Brambila-Paz, P.E. Newstead, R. Thomas, editors), Moduli Spaces, LMS Lecture Notes Series 411, Cambridge University Press, 2014.
  8. (with A. Dancer and J.E. Andersen, editors), Geometry and Physics: A Festschrift in honour of Nigel Hitchin, 2 volumes, Oxford University Press, 2018.

Thesis

 

Other documents

  1. Representations of Surface Groups: background material for AIM Workshop. Notes for the Workshop: Representations of Surface Groups at the American institute of Mathematics, Palo Alto, California, 2007.