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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 The Simons Center for Geometry and Physics is a center for theoretical physics and mathematics at Stony Brook University in New York. The focus of the center is mathematical physics and the interface of geometry and physics. It was founded in 2 ...
at
Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system's ...
.


Life

Morgan received his B.A. in 1968 and Ph.D. in 1969, both from Rice University. His Ph.D. thesis, entitled ''Stable tangential homotopy equivalences'', was written under the supervision of
Morton L. Curtis Morton Landers Curtis (November 11, 1921 – February 4, 1989) was an American mathematician, an expert on group theory and the William Lewis Moody, Jr., W. L. Moody, Jr. Professor of Mathematics at Rice University.
. He was an instructor at Princeton University from 1969 to 1972, and an assistant professor at MIT from 1972 to 1974. 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. Morgan is a member of the
Simons Center for Geometry and Physics The Simons Center for Geometry and Physics is a center for theoretical physics and mathematics at Stony Brook University in New York. The focus of the center is mathematical physics and the interface of geometry and physics. It was founded in 2 ...
at
Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system's ...
and served as its founding director from 2009 to 2016. From 1974 to 1976, Morgan was a
Sloan Research Fellow The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...
. In 2008, he was awarded a Gauss Lectureship by the German Mathematical Society. In 2009 he was elected to the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
. In 2012 he became a fellow of the American Mathematical Society. Morgan is a Member of the
European Academy of Sciences European, or Europeans, or Europeneans, may refer to: In general * ''European'', an adjective referring to something of, from, or related to Europe ** Ethnic groups in Europe ** Demographics of Europe ** European cuisine, the cuisines of Europe ...
.


Mathematical contributions

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 In mathematics, in particular abstract algebra and topology, a differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. __TOC__ Definition A differential graded alg ...
. 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 simply-connected compact Kähler manifolds. Their primary result is that the real homotopy type of such a space is determined by its
cohomology ring In mathematics, specifically algebraic topology, the cohomology ring of a topological space ''X'' is a ring formed from the cohomology groups of ''X'' together with the cup product serving as the ring multiplication. Here 'cohomology' is usually und ...
. 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. 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. 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. Starting in 2003, and culminating in a 2008 publication,
Bruce Kleiner Bruce Alan Kleiner is an American mathematician, working in differential geometry and topology and geometric group theory. He received his Ph.D. in 1990 from the University of California, Berkeley. His advisor was Wu-Yi Hsiang. Kleiner is ...
and
John Lott John Richard Lott Jr. (born May 8, 1958) is an American economist, political commentator, and gun rights advocate. Lott was formerly employed at various academic institutions and at the American Enterprise Institute conservative think tank. He ...
posted detailed annotations of Perelman's first two papers to their websites, covering his work on the proof of the geometrization conjecture. In 2006,
Huai-Dong Cao Huai-Dong Cao (born 8 November 1959, in Jiangsu) is a Chinese–American mathematician. He is the A. Everett Pitcher Professor of Mathematics at Lehigh University. He is known for his research contributions to the Ricci flow, a topic in the field ...
and
Xi-Ping Zhu Zhu Xiping (born 1962 in Shixing, Guangdong) is a Chinese mathematician. He is a professor of Mathematics at Sun Yat-sen University, China. Poincaré conjecture In 2002 and 2003, Grigori Perelman posted three preprints to the arXiv claiming a r ...
published an exposition of Hamilton and Perelman's works, also covering Perelman's first two articles. In 2007, Morgan and
Gang Tian Tian Gang (; born November 24, 1958) is a Chinese mathematician. He is a professor of mathematics at Peking University and Higgins Professor Emeritus at Princeton University. He is known for contributions to the mathematical fields of Kähler g ...
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." The level of detail in Morgan and Tian's work was criticized in 2015 by mathematician
Abbas Bahri Abbas Bahri (1 January 1955 – 10 January 2016) was a Tunisian mathematician. He was the winner of the Fermat Prize and the Langevin Prize in mathematics. He was a professor of mathematics at Rutgers University. He mainly studied the calcul ...
, who found a counterexample to one of their claims corresponding to Perelman's third paper. The error, originating in the incorrect calculation of a geometric evolution equation, was thereafter fixed by Morgan and Tian.


Selected publications

Articles. * Pierre Deligne, Phillip Griffiths, John Morgan, and Dennis Sullivan. ''Real homotopy theory of Kähler manifolds.'' Invent. Math. 29 (1975), no. 3, 245–274. * John W. Morgan. ''The algebraic topology of smooth algebraic varieties.'' Inst. Hautes Études Sci. Publ. Math. No. 48 (1978), 137–204. ** 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 -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. 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. * 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. * 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 : smooth classification. With the collaboration of Millie Niss. Lecture Notes in Mathematics, 1545. Springer-Verlag, Berlin, 1993. viii+224 pp. * John W. Morgan, Tomasz Mrowka, and Daniel Ruberman. The -moduli space and a vanishing theorem for Donaldson polynomial invariants. Monographs in Geometry and Topology, II. International Press, Cambridge, MA, 1994. ii+222 pp. * 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. * 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. *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. **John Morgan and Gang Tian. Correction to Section 19.2 of Ricci Flow and the Poincare Conjecture. * 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. * Phillip Griffiths and John Morgan. Rational homotopy theory and differential forms. Second edition. Progress in Mathematics, 16. Springer, New York, 2013. xii+224 pp. * 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.


References


External links


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at Columbia University {{DEFAULTSORT:Morgan, John 20th-century American mathematicians 21st-century American mathematicians Columbia University faculty Stony Brook University faculty Geometers Living people Rice University alumni Topologists Fellows of the American Mathematical Society Members of the United States National Academy of Sciences 1946 births Princeton University faculty Massachusetts Institute of Technology faculty