John Morgan (mathematician)

John Willard Morgan (born March 21, 1946 in Philadelphia ) is an American mathematician who studies topology and algebraic geometry .

Morgan studied at Rice University , where he made his bachelor's degree in 1969 and received his doctorate in 1969 with Morton L. Curtis ( stable tangential homotopy equivalences ). From 1969 to 1972 he was an instructor at Princeton University and from 1972 to 1974 Assistant Professor at the Massachusetts Institute of Technology (MIT). From 1974 he was associate professor and from 1977 professor at Columbia University . Among other things, he was visiting professor at the Institut des Hautes Études Scientifiques (IHES, 2000/2001, 1974 to 1976), at the Institute for Advanced Study (1996/97), at Princeton University (1994 to 1996), at Harvard University (1989 / 1990), at the Mathematical Sciences Research Institute (MSRI, 1984/1985) and at the University of Paris-Süd (1975/76).

In 2006 he and Tian Gang formed one of the three teams that scrutinized the proof of the Poincaré conjecture by Grigori Perelman . With Zoltán Szabó and Clifford Taubes he proved the Thom conjecture in 1994 , independently of Peter Kronheimer and Tomasz Mrowka .

From 1974 to 1976 he was a Sloan Research Fellow . In 1986 he was invited speaker at the International Congress of Mathematicians (ICM) in Berkeley ( Trees and hyperbolic geometry ) and in 2006 in Madrid, where he confirmed Perelman's solution to the Poincaré conjecture. He was an editor of Inventiones Mathematicae , the Journal of the AMS, and Geometry and Topology , among others . In 2009 he received the Levi L. Conant Prize and was elected to the National Academy of Sciences . In 2008 he gave the Gauss lecture at the DMV . He is a fellow of the American Mathematical Society . In 2018 he was on the Fields Medal Award Committee .

Fonts

with Phillip Griffiths : Rational homotopy theory and differential forms , Progress in Mathematics, Vol. 16, Birkhäuser, Boston, 1981. ISBN 3-7643-3041-4
Editor with Hyman Bass : The Smith conjecture , Papers presented at the symposium held at Columbia University, New York, 1979, Academic Press 1984
with Tomasz Mrowka, Daniel Ruberman: The L ² -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
The algebraic topology of smooth algebraic varieties , Publications Mathématiques de l'IHÉS, Vol. 48, 1978, pp. 137-204.
with Robert Friedman : Smooth four-manifolds and complex surfaces , Springer, Results of Mathematics and their Border Areas, 1994. ISBN 3-540-57058-6
The Seiberg-Witten equations and applications to the topology of smooth four-manifolds , Mathematical Notes, Vol. 44, Princeton University Press 1996. ISBN 0-691-02597-5
with Tian Gang: Ricci Flow and the Poincaré Conjecture , Clay Mathematics Institute, 2007
Recent Progress on the Poincare conjecture and the classification of 3-manifolds ( PDF file; 293 kB), Bulletin AMS, Vol. 42, 2005, Issue 1 (won the Conant Prize)

^ Morgan, Szabo, Taubes: A product formula for the Seiberg-Witten Invariants and the generalized Thom Conjecture , Journal of Differential Geometry, Vol. 44, 1996, pp. 706-788