John Willard Morgan is an American mathematician, well-known for his contributions to topology and geometry. He is currently Professor and Chair of the Mathematics Department at Columbia University.
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Life
He 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. 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. He is an editor of the Journal of the American Mathematical Society and Geometry and Topology.
Work
He collaborated with Gang Tian in verifying Grigori Perelman's proof of the Poincaré conjecture.[1] The Morgan-Tian team was one of three teams formed for this purpose; the other teams were those of Huai-Dong Cao and Xi-Ping Zhu, and Bruce Kleiner and John Lott. Morgan gave a plenary lecture at the International Congress of Mathematicians in Madrid on August 24 2006, declaring that "in 2003, Perelman solved the Poincaré Conjecture."
Selected publications
Articles
- Pierre Deligne, Phillip Griffiths, John Morgan, Dennis Sullivan, Real homotopy theory of Kähler manifolds, Inventiones Mathematicae 29 (1975), no. 3, 245–274. MR0382702
- John W. Morgan, The algebraic topology of smooth algebraic varieties, Publications Mathématiques de l'IHÉS 48 (1978), 137–204. MR0516917
- John W. Morgan, Trees and hyperbolic geometry, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, CA, 1986), 590–597, Amer. Math. Soc., Providence, RI, 1987. MR0934260
- John W. Morgan, Zoltán Szabó, Clifford Henry Taubes, A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture, Journal of Differential Geometry 44 (1996), no. 4, 706–788. MR1438191
- John W. Morgan, Recent progress on the Poincaré conjecture and the classification of 3-manifolds, Bulletin of the American Mathematical Society 42 (2005), no. 1, 57–78. MR2115067
Books
- Phillip A. Griffiths, John W. Morgan, "Rational homotopy theory and differential forms", Progress in Mathematics, vol. 16, Birkhäuser, Boston, MA, 1981. ISBN 3-7643-3041-4
- "The Smith conjecture", Papers presented at the symposium held at Columbia University, New York, 1979. Edited by John W. Morgan and Hyman Bass. Pure and Applied Mathematics, vol. 112, Academic Press, Orlando, FL, 1984. ISBN 0-12-506980-4
- John W. Morgan, Tomasz Mrowka, 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. ISBN 1-57146-006-3
- Robert Friedman, John W. Morgan, "Smooth four-manifolds and complex surfaces", Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 27, Springer-Verlag, Berlin, 1994. ISBN 3-540-57058-6
- John W. Morgan, "The Seiberg-Witten equations and applications to the topology of smooth four-manifolds", Mathematical Notes, vol. 44, Princeton University Press, Princeton, NJ, 1996. ISBN 0-691-02597-5
- Morgan, John; Gang Tian (2007). Ricci Flow and the Poincaré Conjecture. Clay Mathematics Institute. ISBN 0821843281.
External links
- John Morgan (mathematician) at the Mathematics Genealogy Project
- Home page at Columbia University
- Biographical sketch at the Chinese University of Hong Kong
- Conference in Honor of the 60th Birthday of John Morgan at Columbia University
