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Carlos Simpson

October 21, 2023

Carlos Tschudi Simpson (born 30 June 1962) is an American mathematician, specializing in algebraic geometry.

Simpson received his Ph.D. in 1987 from Harvard University, where he was supervised by Wilfried Schmid; his thesis was titled Systems of Hodge Bundles and Uniformization.[1] He became a professor[clarification needed] at the University of Toulouse III (Paul Sabatier University) and then at the University of Nice. He is research director of the Centre national de la recherche scientifique.

He works on moduli spaces of vector bundles, higher non-abelian de Rham cohomology (Hodge theory), the theory of higher categories and computer verification of mathematical proofs (e.g. verification of proofs within Zermelo–Fraenkel set theory using Coq). In his Ph.D. dissertation, Simpson studied the notion of system of Hodge bundles, which can be seen as a special case of the higher dimensional generalization of Higgs bundles introduced earlier by Nigel Hitchin.[2] The Simpson correspondence (or the Corlette-Simpson correspondence, named after Kevin Corlette and Simpson) is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, complex algebraic curve.

The Deligne–Simpson Problem, an algebraic problem associated with monodromy matrices, is named after Carlos Simpson and Pierre Deligne.[3]

Simpson was an Invited Speaker with talk Nonabelian Hodge theory at the International Congress of Mathematicians in 1990 at Kyoto. In 2015 he received the Sophie Germain Prize.

Selected publications Edit

  • Simpson, Carlos (1988). "Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization". Journal of the American Mathematical Society. 1 (4): 867–918. doi:10.2307/1990994. JSTOR 1990994. MR 0944577.
  • Simpson, Carlos (1990). "Transcendental aspects of the Riemann–Hilbert correspondence". Illinois Journal of Mathematics. 34 (2): 368–391. doi:10.1215/ijm/1255988271. MR 1046569.
  • Simpson, Carlos (1990). "Harmonic bundles on noncompact curves". Journal of the American Mathematical Society. 3 (3): 713–770. doi:10.2307/1990935. JSTOR 1990935. MR 1040197.
  • Simpson, Carlos (1991). Asymptotic behavior of monodromy: singularly perturbed differential equations on a Riemann surface. Lecture Notes in Mathematics. Vol. 1502. Springer Verlag. ISBN 3-540-55009-7. MR 1166192.
  • Simpson, Carlos (1992). "Higgs bundles and local systems". Publications Mathématiques de l'IHÉS. 75: 5–95. doi:10.1007/bf02699491. MR 1179076. S2CID 56417181.
  • Simpson, Carlos (1993). "Subspaces of moduli spaces of rank one local systems". Annales Scientifiques de l'École Normale Supérieure. 4. 26 (3): 361–401. doi:10.24033/asens.1675. MR 1222278.
  • Simpson, Carlos (1994). "Moduli of representations of the fundamental group of a smooth projective variety. I." Publications Mathématiques de l'IHÉS. 79: 47–129. doi:10.1007/bf02698887. MR 1307297. S2CID 122031663.
  • Simpson, Carlos (1994). "Moduli of representations of the fundamental group of a smooth projective variety. II". Publications Mathématiques de l'IHÉS. 80: 5–79. doi:10.1007/bf02698895. MR 1320603. S2CID 189763976.
  • Simpson, Carlos (1997), "The Hodge filtration on nonabelian cohomology", Algebraic geometry (Santa Cruz 1995), Proc. Sympos. Pure Math., vol. 62, Part 2, American Mathematical Society, pp. 217–281, arXiv:alg-geom/9604005, doi:10.1090/pspum/062.2/1492538, MR 1492538, S2CID 2659059
  • Simpson, Carlos (2012). Homotopy theory of higher categories. New Mathematical Monographs. Vol. 19. Cambridge: Cambridge University Press. ISBN 9781139502191. MR 2883823.

References Edit

  1. ^ Carlos Simpson at the Mathematics Genealogy Project
  2. ^ Bradlow, Steven B.; García-Prada, Oscar; Gothen, Peter B. (2007), "What is a Higgs bundle ?" (PDF), Notices of the American Mathematical Society, 54: 980–981
  3. ^ Kostov, Vladimir Petrov (2004). "The Deligne-Simpson problem—a survey". Journal of Algebra. 281 (1): 83–108. arXiv:math/0206298. doi:10.1016/j.jalgebra.2004.07.013. MR 2091962. S2CID 119634752.

External links Edit

  • Carlos Simpson publications indexed by Google Scholar
  • "Carlos Simpson's homepage at the University of Nice".
  • "Carlos Simpson – An overview of the structure at infinity of representation spaces". YouTube.com. 2014.

October 21, 2023
carlos, simpson, carlos, tschudi, simpson, born, june, 1962, american, mathematician, specializing, algebraic, geometry, simpson, received, 1987, from, harvard, university, where, supervised, wilfried, schmid, thesis, titled, systems, hodge, bundles, uniformiz. Carlos Tschudi Simpson born 30 June 1962 is an American mathematician specializing in algebraic geometry Simpson received his Ph D in 1987 from Harvard University where he was supervised by Wilfried Schmid his thesis was titled Systems of Hodge Bundles and Uniformization 1 He became a professor clarification needed at the University of Toulouse III Paul Sabatier University and then at the University of Nice He is research director of the Centre national de la recherche scientifique He works on moduli spaces of vector bundles higher non abelian de Rham cohomology Hodge theory the theory of higher categories and computer verification of mathematical proofs e g verification of proofs within Zermelo Fraenkel set theory using Coq In his Ph D dissertation Simpson studied the notion of system of Hodge bundles which can be seen as a special case of the higher dimensional generalization of Higgs bundles introduced earlier by Nigel Hitchin 2 The Simpson correspondence or the Corlette Simpson correspondence named after Kevin Corlette and Simpson is a correspondence between Higgs bundles and representations of the fundamental group of a smooth complex algebraic curve The Deligne Simpson Problem an algebraic problem associated with monodromy matrices is named after Carlos Simpson and Pierre Deligne 3 Simpson was an Invited Speaker with talk Nonabelian Hodge theory at the International Congress of Mathematicians in 1990 at Kyoto In 2015 he received the Sophie Germain Prize Selected publications EditSimpson Carlos 1988 Constructing variations of Hodge structure using Yang Mills theory and applications to uniformization Journal of the American Mathematical Society 1 4 867 918 doi 10 2307 1990994 JSTOR 1990994 MR 0944577 Simpson Carlos 1990 Transcendental aspects of the Riemann Hilbert correspondence Illinois Journal of Mathematics 34 2 368 391 doi 10 1215 ijm 1255988271 MR 1046569 Simpson Carlos 1990 Harmonic bundles on noncompact curves Journal of the American Mathematical Society 3 3 713 770 doi 10 2307 1990935 JSTOR 1990935 MR 1040197 Simpson Carlos 1991 Asymptotic behavior of monodromy singularly perturbed differential equations on a Riemann surface Lecture Notes in Mathematics Vol 1502 Springer Verlag ISBN 3 540 55009 7 MR 1166192 Simpson Carlos 1992 Higgs bundles and local systems Publications Mathematiques de l IHES 75 5 95 doi 10 1007 bf02699491 MR 1179076 S2CID 56417181 Simpson Carlos 1993 Subspaces of moduli spaces of rank one local systems Annales Scientifiques de l Ecole Normale Superieure 4 26 3 361 401 doi 10 24033 asens 1675 MR 1222278 Simpson Carlos 1994 Moduli of representations of the fundamental group of a smooth projective variety I Publications Mathematiques de l IHES 79 47 129 doi 10 1007 bf02698887 MR 1307297 S2CID 122031663 Simpson Carlos 1994 Moduli of representations of the fundamental group of a smooth projective variety II Publications Mathematiques de l IHES 80 5 79 doi 10 1007 bf02698895 MR 1320603 S2CID 189763976 Simpson Carlos 1997 The Hodge filtration on nonabelian cohomology Algebraic geometry Santa Cruz 1995 Proc Sympos Pure Math vol 62 Part 2 American Mathematical Society pp 217 281 arXiv alg geom 9604005 doi 10 1090 pspum 062 2 1492538 MR 1492538 S2CID 2659059 Simpson Carlos 2012 Homotopy theory of higher categories New Mathematical Monographs Vol 19 Cambridge Cambridge University Press ISBN 9781139502191 MR 2883823 References Edit Carlos Simpson at the Mathematics Genealogy Project Bradlow Steven B Garcia Prada Oscar Gothen Peter B 2007 What is a Higgs bundle PDF Notices of the American Mathematical Society 54 980 981 Kostov Vladimir Petrov 2004 The Deligne Simpson problem a survey Journal of Algebra 281 1 83 108 arXiv math 0206298 doi 10 1016 j jalgebra 2004 07 013 MR 2091962 S2CID 119634752 External links EditCarlos Simpson publications indexed by Google Scholar Carlos Simpson s homepage at the University of Nice Carlos Simpson An overview of the structure at infinity of representation spaces YouTube com 2014 Retrieved from https en wikipedia org w index php title Carlos Simpson amp oldid 1149834973, wikipedia, wiki, book, books, library,

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