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John Morgan (mathematician)

April 16, 2024

John Willard Morgan (born March 21, 1946) is an American mathematician known for his contributions to topology and geometry. He is a Professor Emeritus at Columbia University and a member of the Simons Center for Geometry and Physics at Stony Brook University.

John Morgan
Born (1946-03-21) March 21, 1946 (age 78)
Philadelphia
NationalityAmerican
Alma materRice University
AwardsSloan Research Fellow (1974)
Gauss Lectureship (2008)
Member of the National Academy of Sciences (2009)
Fellow of the American Mathematical Society (2012)
Scientific career
FieldsMathematics
InstitutionsStony Brook University
Columbia University
Doctoral advisorMorton L. Curtis
Doctoral studentsSadayoshi Kojima [ja]
Peter Ozsváth
Zoltán Szabó

Life edit

Morgan received his B.A. in 1968 and Ph.D. in 1969, both from Rice University.[1][2][3] His Ph.D. thesis, entitled Stable tangential homotopy equivalences, was written under the supervision of Morton L. Curtis.[1][2] He was an instructor at Princeton University from 1969 to 1972, and an assistant professor at MIT from 1972 to 1974.[1][3][4] He has been on the faculty at Columbia University since 1974, serving as the Chair of the Department of Mathematics from 1989 to 1991 and becoming Professor Emeritus in 2010.[1][3][4] Morgan is a member of the Simons Center for Geometry and Physics at Stony Brook University and served as its founding director from 2009 to 2016.[3][4]

From 1974 to 1976, Morgan was a Sloan Research Fellow.[1] In 2008, he was awarded a Gauss Lectureship by the German Mathematical Society. In 2009 he was elected to the National Academy of Sciences.[4] In 2012 he became a fellow of the American Mathematical Society.[5] Morgan is a Member of the European Academy of Sciences.[1]

Mathematical contributions edit

Morgan's best-known work deals with the topology of complex manifolds and algebraic varieties. In the 1970s, Dennis Sullivan developed the notion of a minimal model of a differential graded algebra.[6] One of the simplest examples of a differential graded algebra is the space of smooth differential forms on a smooth manifold, so that Sullivan was able to apply his theory to understand the topology of smooth manifolds. In the setting of Kähler geometry, due to the corresponding version of the Poincaré lemma, this differential graded algebra has a decomposition into holomorphic and anti-holomorphic parts. In collaboration with Pierre Deligne, Phillip Griffiths, and Sullivan, Morgan used this decomposition to apply Sullivan's theory to study the topology of compact Kähler manifolds. Their primary result is that the real homotopy type of such a space is determined by its cohomology ring. Morgan later extended this analysis to the setting of smooth complex algebraic varieties, using Deligne's formulation of mixed Hodge structures to extend the Kähler decomposition of smooth differential forms and of the exterior derivative.[7]

In 2002 and 2003, Grigori Perelman posted three papers to the arXiv which purported to use Richard Hamilton's theory of Ricci flow solve the geometrization conjecture in three-dimensional topology, of which the renowned Poincaré conjecture is a special case.[8] Perelman's first two papers claimed to prove the geometrization conjecture; the third paper gives an argument which would obviate the technical work in the second half of the second paper in order to give a shortcut to prove the Poincaré conjecture. Many mathematicians found Perelman's work to be hard to follow due to a lack of detail on a number of technical points.[citation needed]

Starting in 2003, and culminating in a 2008 publication, Bruce Kleiner and John Lott posted detailed annotations of Perelman's first two papers to their websites, covering his work on the proof of the geometrization conjecture.[9] In 2006, Huai-Dong Cao and Xi-Ping Zhu published an exposition of Hamilton and Perelman's works, also covering Perelman's first two articles.[10] In 2007, Morgan and Gang Tian published a book on Perelman's first paper, the first half of his second paper, and his third paper. As such, they covered the proof of the Poincaré conjecture. In 2014, they published a book covering the remaining details for the geometrization conjecture. In 2006, Morgan gave a plenary lecture at the International Congress of Mathematicians in Madrid, saying that Perelman's work had "now been thoroughly checked. He has proved the Poincaré conjecture."[11] The level of detail in Morgan and Tian's work was criticized in 2015 by mathematician Abbas Bahri, who found a counterexample to one of their claims corresponding to Perelman's third paper.[12][13] The error, originating in the incorrect calculation of a geometric evolution equation, was thereafter fixed by Morgan and Tian.[citation needed]

Selected publications edit

Articles.

  • Pierre Deligne, Phillip Griffiths, John Morgan, and Dennis Sullivan. Real homotopy theory of Kähler manifolds. Invent. Math. 29 (1975), no. 3, 245–274. MR0382702
  • John W. Morgan. The algebraic topology of smooth algebraic varieties. Inst. Hautes Études Sci. Publ. Math. No. 48 (1978), 137–204. MR0516917
    • John W. Morgan. Correction to: "The algebraic topology of smooth algebraic varieties". Inst. Hautes Études Sci. Publ. Math. No. 64 (1986), 185.
  • John W. Morgan and Peter B. Shalen. Valuations, trees, and degenerations of hyperbolic structures. I. Ann. of Math. (2) 120 (1984), no. 3, 401–476.
  • Marc Culler and John W. Morgan. Group actions on ℝ-trees. Proc. London Math. Soc. (3) 55 (1987), no. 3, 571–604.
  • John W. Morgan, Zoltán Szabó, Clifford Henry Taubes. A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture. J. Differential Geom. 44 (1996), no. 4, 706–788. MR1438191

Survey articles.

  • John W. Morgan. The rational homotopy theory of smooth, complex projective varieties (following P. Deligne, P. Griffiths, J. Morgan, and D. Sullivan). Séminaire Bourbaki, Vol. 1975/76, 28ème année, Exp. No. 475, pp. 69–80. Lecture Notes in Math., Vol. 567, Springer, Berlin, 1977.
  • John W. Morgan. On Thurston's uniformization theorem for three-dimensional manifolds. The Smith conjecture (New York, 1979), 37–125, Pure Appl. Math., 112, Academic Press, Orlando, FL, 1984.
  • John W. Morgan. Trees and hyperbolic geometry. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 590–597, Amer. Math. Soc., Providence, RI, 1987. MR0934260
  • John W. Morgan. Λ-trees and their applications. Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 1, 87–112.
  • Pierre Deligne and John W. Morgan. Notes on supersymmetry (following Joseph Bernstein). Quantum fields and strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), 41–97, Amer. Math. Soc., Providence, RI, 1999.
  • John W. Morgan. Recent progress on the Poincaré conjecture and the classification of 3-manifolds. Bull. Amer. Math. Soc. (N.S.) 42 (2005), no. 1, 57–78. MR2115067
  • John W. Morgan. The Poincaré conjecture. International Congress of Mathematicians. Vol. I, 713–736, Eur. Math. Soc., Zürich, 2007.

Books.

  • John W. Morgan and Kieran G. O'Grady. Differential topology of complex surfaces. Elliptic surfaces with pg = 1: smooth classification. With the collaboration of Millie Niss. Lecture Notes in Mathematics, 1545. Springer-Verlag, Berlin, 1993. viii+224 pp. ISBN 3-540-56674-0
  • John W. Morgan, Tomasz Mrowka, and Daniel Ruberman. The L2-moduli space and a vanishing theorem for Donaldson polynomial invariants. Monographs in Geometry and Topology, II. International Press, Cambridge, MA, 1994. ii+222 pp. ISBN 1-57146-006-3
  • Robert Friedman and John W. Morgan. Smooth four-manifolds and complex surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 27. Springer-Verlag, Berlin, 1994. x+520 pp. ISBN 3-540-57058-6
  • John W. Morgan. The Seiberg-Witten equations and applications to the topology of smooth four-manifolds. Mathematical Notes, 44. Princeton University Press, Princeton, NJ, 1996. viii+128 pp. ISBN 0-691-02597-5
  • John Morgan and Gang Tian. Ricci flow and the Poincaré conjecture. Clay Mathematics Monographs, 3. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2007. xlii+521 pp. ISBN 978-0-8218-4328-4
    • John Morgan and Gang Tian. Correction to Section 19.2 of Ricci Flow and the Poincare Conjecture. arXiv:1512.00699
  • John W. Morgan and Frederick Tsz-Ho Fong. Ricci flow and geometrization of 3-manifolds. University Lecture Series, 53. American Mathematical Society, Providence, RI, 2010. x+150 pp. ISBN 978-0-8218-4963-7
  • Phillip Griffiths and John Morgan. Rational homotopy theory and differential forms. Second edition. Progress in Mathematics, 16. Springer, New York, 2013. xii+224 pp. ISBN 978-1-4614-8467-7, 978-1-4614-8468-4[14]
  • John Morgan and Gang Tian. The geometrization conjecture. Clay Mathematics Monographs, 5. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2014. x+291 pp. ISBN 978-0-8218-5201-9

References edit

  1. ^ a b c d e f "Biographical Sketch: John Morgan" (PDF). Chinese University of Hong Kong. Retrieved January 27, 2021.
  2. ^ a b John Morgan at the Mathematics Genealogy Project
  3. ^ a b c d "John Morgan". Simons Center for Geometry and Physics at Stony Brook University. Retrieved January 27, 2021.
  4. ^ a b c d "The Founding Director". Simons Center for Geometry and Physics at Stony Brook University. Retrieved January 27, 2021.
  5. ^ List of Fellows of the American Mathematical Society, retrieved 2013-02-10.
  6. ^ Dennis Sullivan. Infinitesimal computations in topology. Inst. Hautes Études Sci. Publ. Math. No. 47 (1977), 269–331
  7. ^ Pierre Deligne. Théorie de Hodge. II. Inst. Hautes Études Sci. Publ. Math. No. 40 (1971), 5–57.
  8. ^ Grisha Perelman. The entropy formula for the Ricci flow and its geometric applications. arXiv:math/0211159
    Grisha Perelman. Ricci flow with surgery on three-manifolds. arXiv:math/0303109
    Grisha Perelman. Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. arXiv:math/0307245
  9. ^ Bruce Kleiner and John Lott. Notes on Perelman's papers. Geom. Topol. 12 (2008), no. 5, 2587–2855.
  10. ^ Huai-Dong Cao and Xi-Ping Zhu. A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow. Asian J. Math. 10 (2006), no. 2, 165–492.
  11. ^ John Morgan. The Poincaré Conjecture (special lecture). Minute 43:40.
  12. ^ Abbas Bahri. Five gaps in mathematics. Adv. Nonlinear Stud. 15 (2015), no. 2, 289–319.
  13. ^ Abbas Bahri. A counterexample to the second inequality of Corollary (19.10) in the monograph "Ricci Flow and the Poincare Conjecture" by J.Morgan and G.Tian. arXiv:1512.02046
  14. ^ Chen, Kuo-Tsai (1983). "Review: Rational homotopy theory and differential forms, by P. A. Griffiths and J. W. Morgan". Bull. Amer. Math. Soc. (N.S.). 8 (3): 496–498. doi:10.1090/s0273-0979-1983-15135-2.

External links edit

  • at Columbia University
  • at Columbia University

April 16, 2024
john, morgan, mathematician, john, willard, morgan, born, march, 1946, american, mathematician, known, contributions, topology, geometry, professor, emeritus, columbia, university, member, simons, center, geometry, physics, stony, brook, university, john, morg. John Willard Morgan born March 21 1946 is an American mathematician known for his contributions to topology and geometry He is a Professor Emeritus at Columbia University and a member of the Simons Center for Geometry and Physics at Stony Brook University John MorganBorn 1946 03 21 March 21 1946 age 78 PhiladelphiaNationalityAmericanAlma materRice UniversityAwardsSloan Research Fellow 1974 Gauss Lectureship 2008 Member of the National Academy of Sciences 2009 Fellow of the American Mathematical Society 2012 Scientific careerFieldsMathematicsInstitutionsStony Brook UniversityColumbia UniversityDoctoral advisorMorton L CurtisDoctoral studentsSadayoshi Kojima ja Peter OzsvathZoltan Szabo Contents 1 Life 2 Mathematical contributions 3 Selected publications 4 References 5 External linksLife editMorgan received his B A in 1968 and Ph D in 1969 both from Rice University 1 2 3 His Ph D thesis entitled Stable tangential homotopy equivalences was written under the supervision of Morton L Curtis 1 2 He was an instructor at Princeton University from 1969 to 1972 and an assistant professor at MIT from 1972 to 1974 1 3 4 He has been on the faculty at Columbia University since 1974 serving as the Chair of the Department of Mathematics from 1989 to 1991 and becoming Professor Emeritus in 2010 1 3 4 Morgan is a member of the Simons Center for Geometry and Physics at Stony Brook University and served as its founding director from 2009 to 2016 3 4 From 1974 to 1976 Morgan was a Sloan Research Fellow 1 In 2008 he was awarded a Gauss Lectureship by the German Mathematical Society In 2009 he was elected to the National Academy of Sciences 4 In 2012 he became a fellow of the American Mathematical Society 5 Morgan is a Member of the European Academy of Sciences 1 Mathematical contributions editMorgan s best known work deals with the topology of complex manifolds and algebraic varieties In the 1970s Dennis Sullivan developed the notion of a minimal model of a differential graded algebra 6 One of the simplest examples of a differential graded algebra is the space of smooth differential forms on a smooth manifold so that Sullivan was able to apply his theory to understand the topology of smooth manifolds In the setting of Kahler geometry due to the corresponding version of the Poincare lemma this differential graded algebra has a decomposition into holomorphic and anti holomorphic parts In collaboration with Pierre Deligne Phillip Griffiths and Sullivan Morgan used this decomposition to apply Sullivan s theory to study the topology of compact Kahler manifolds Their primary result is that the real homotopy type of such a space is determined by its cohomology ring Morgan later extended this analysis to the setting of smooth complex algebraic varieties using Deligne s formulation of mixed Hodge structures to extend the Kahler decomposition of smooth differential forms and of the exterior derivative 7 In 2002 and 2003 Grigori Perelman posted three papers to the arXiv which purported to use Richard Hamilton s theory of Ricci flow solve the geometrization conjecture in three dimensional topology of which the renowned Poincare conjecture is a special case 8 Perelman s first two papers claimed to prove the geometrization conjecture the third paper gives an argument which would obviate the technical work in the second half of the second paper in order to give a shortcut to prove the Poincare conjecture Many mathematicians found Perelman s work to be hard to follow due to a lack of detail on a number of technical points citation needed Starting in 2003 and culminating in a 2008 publication Bruce Kleiner and John Lott posted detailed annotations of Perelman s first two papers to their websites covering his work on the proof of the geometrization conjecture 9 In 2006 Huai Dong Cao and Xi Ping Zhu published an exposition of Hamilton and Perelman s works also covering Perelman s first two articles 10 In 2007 Morgan and Gang Tian published a book on Perelman s first paper the first half of his second paper and his third paper As such they covered the proof of the Poincare conjecture In 2014 they published a book covering the remaining details for the geometrization conjecture In 2006 Morgan gave a plenary lecture at the International Congress of Mathematicians in Madrid saying that Perelman s work had now been thoroughly checked He has proved the Poincare conjecture 11 The level of detail in Morgan and Tian s work was criticized in 2015 by mathematician Abbas Bahri who found a counterexample to one of their claims corresponding to Perelman s third paper 12 13 The error originating in the incorrect calculation of a geometric evolution equation was thereafter fixed by Morgan and Tian citation needed Selected publications editArticles Pierre Deligne Phillip Griffiths John Morgan and Dennis Sullivan Real homotopy theory of Kahler manifolds Invent Math 29 1975 no 3 245 274 MR0382702 John W Morgan The algebraic topology of smooth algebraic varieties Inst Hautes Etudes Sci Publ Math No 48 1978 137 204 MR0516917 John W Morgan Correction to The algebraic topology of smooth algebraic varieties Inst Hautes Etudes Sci Publ Math No 64 1986 185 John W Morgan and Peter B Shalen Valuations trees and degenerations of hyperbolic structures I Ann of Math 2 120 1984 no 3 401 476 Marc Culler and John W Morgan Group actions on ℝ trees Proc London Math Soc 3 55 1987 no 3 571 604 John W Morgan Zoltan Szabo Clifford Henry Taubes A product formula for the Seiberg Witten invariants and the generalized Thom conjecture J Differential Geom 44 1996 no 4 706 788 MR1438191Survey articles John W Morgan The rational homotopy theory of smooth complex projective varieties following P Deligne P Griffiths J Morgan and D Sullivan Seminaire Bourbaki Vol 1975 76 28eme annee Exp No 475 pp 69 80 Lecture Notes in Math Vol 567 Springer Berlin 1977 John W Morgan On Thurston s uniformization theorem for three dimensional manifolds The Smith conjecture New York 1979 37 125 Pure Appl Math 112 Academic Press Orlando FL 1984 John W Morgan Trees and hyperbolic geometry Proceedings of the International Congress of Mathematicians Vol 1 2 Berkeley Calif 1986 590 597 Amer Math Soc Providence RI 1987 MR0934260 John W Morgan L trees and their applications Bull Amer Math Soc N S 26 1992 no 1 87 112 Pierre Deligne and John W Morgan Notes on supersymmetry following Joseph Bernstein Quantum fields and strings a course for mathematicians Vol 1 2 Princeton NJ 1996 1997 41 97 Amer Math Soc Providence RI 1999 John W Morgan Recent progress on the Poincare conjecture and the classification of 3 manifolds Bull Amer Math Soc N S 42 2005 no 1 57 78 MR2115067 John W Morgan The Poincare conjecture International Congress of Mathematicians Vol I 713 736 Eur Math Soc Zurich 2007 Books John W Morgan and Kieran G O Grady Differential topology of complex surfaces Elliptic surfaces with pg 1 smooth classification With the collaboration of Millie Niss Lecture Notes in Mathematics 1545 Springer Verlag Berlin 1993 viii 224 pp ISBN 3 540 56674 0 John W Morgan Tomasz Mrowka and Daniel Ruberman The L2 moduli space and a vanishing theorem for Donaldson polynomial invariants Monographs in Geometry and Topology II International Press Cambridge MA 1994 ii 222 pp ISBN 1 57146 006 3 Robert Friedman and John W Morgan Smooth four manifolds and complex surfaces Ergebnisse der Mathematik und ihrer Grenzgebiete 3 27 Springer Verlag Berlin 1994 x 520 pp ISBN 3 540 57058 6 John W Morgan The Seiberg Witten equations and applications to the topology of smooth four manifolds Mathematical Notes 44 Princeton University Press Princeton NJ 1996 viii 128 pp ISBN 0 691 02597 5 John Morgan and Gang Tian Ricci flow and the Poincare conjecture Clay Mathematics Monographs 3 American Mathematical Society Providence RI Clay Mathematics Institute Cambridge MA 2007 xlii 521 pp ISBN 978 0 8218 4328 4 John Morgan and Gang Tian Correction to Section 19 2 of Ricci Flow and the Poincare Conjecture arXiv 1512 00699 John W Morgan and Frederick Tsz Ho Fong Ricci flow and geometrization of 3 manifolds University Lecture Series 53 American Mathematical Society Providence RI 2010 x 150 pp ISBN 978 0 8218 4963 7 Phillip Griffiths and John Morgan Rational homotopy theory and differential forms Second edition Progress in Mathematics 16 Springer New York 2013 xii 224 pp ISBN 978 1 4614 8467 7 978 1 4614 8468 4 14 John Morgan and Gang Tian The geometrization conjecture Clay Mathematics Monographs 5 American Mathematical Society Providence RI Clay Mathematics Institute Cambridge MA 2014 x 291 pp ISBN 978 0 8218 5201 9References edit a b c d e f Biographical Sketch John Morgan PDF Chinese University of Hong Kong Retrieved January 27 2021 a b John Morgan at the Mathematics Genealogy Project a b c d John Morgan Simons Center for Geometry and Physics at Stony Brook University Retrieved January 27 2021 a b c d The Founding Director Simons Center for Geometry and Physics at Stony Brook University Retrieved January 27 2021 List of Fellows of the American Mathematical Society retrieved 2013 02 10 Dennis Sullivan Infinitesimal computations in topology Inst Hautes Etudes Sci Publ Math No 47 1977 269 331 Pierre Deligne Theorie de Hodge II Inst Hautes Etudes Sci Publ Math No 40 1971 5 57 Grisha Perelman The entropy formula for the Ricci flow and its geometric applications arXiv math 0211159Grisha Perelman Ricci flow with surgery on three manifolds arXiv math 0303109Grisha Perelman Finite extinction time for the solutions to the Ricci flow on certain three manifolds arXiv math 0307245 Bruce Kleiner and John Lott Notes on Perelman s papers Geom Topol 12 2008 no 5 2587 2855 Huai Dong Cao and Xi Ping Zhu A complete proof of the Poincare and geometrization conjectures application of the Hamilton Perelman theory of the Ricci flow Asian J Math 10 2006 no 2 165 492 John Morgan The Poincare Conjecture special lecture Minute 43 40 Abbas Bahri Five gaps in mathematics Adv Nonlinear Stud 15 2015 no 2 289 319 Abbas Bahri A counterexample to the second inequality of Corollary 19 10 in the monograph Ricci Flow and the Poincare Conjecture by J Morgan and G Tian arXiv 1512 02046 Chen Kuo Tsai 1983 Review Rational homotopy theory and differential forms by P A Griffiths and J W Morgan Bull Amer Math Soc N S 8 3 496 498 doi 10 1090 s0273 0979 1983 15135 2 External links editHome page at Columbia University Conference in Honor of the 60th Birthday of John Morgan at Columbia University Retrieved from https en wikipedia org w index php title John Morgan mathematician amp oldid 1217696885, wikipedia, wiki, book, books, library,

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