William Thurston
William Paul Thurston ( born October 30, 1946 in Washington, DC; † August 21, 2012 in Rochester, New York ) was an American mathematician.
From him the idea of geometrization for the classification of closed three-dimensional manifolds comes from. For this he received the Fields Medal in 1982. His theory building linked previously viewed as separate mathematical areas with the theory of three-dimensional manifolds.
Life
Thurston studied at New College in Sarasota, Florida ( Bachelor's degree in 1967 ) and then at Morris Hirsch and Stephen Smale at the University of Berkeley, where he received his doctorate in 1972 with a thesis on foliations special 3-manifolds ( Foliations of 3 - manifolds Which are circle bundles ). 1972/73 he was in Princeton at the Institute for Advanced Study. In 1973 he was Assistant Professor at the Massachusetts Institute of Technology (MIT) in 1974 and Professor of Mathematics at Princeton University. Most recently, he was a professor at Cornell University.
In his speech to the award of the Fields Medal to Thurston 1982 CTC Wall emphasizes that Thurston with " fantastic geometric intuition and vision " to the field of topology, two - and three-dimensional manifolds revolutionized. Thurston particular clarified the central role of hyperbolic manifolds (ie manifolds with a metric of constant negative curvature ) in the three-dimensional case. The far largely insulated from the topology theory of discrete groups of isometries of hyperbolic space ( Klein groups) thus became a central theme of the three-dimensional topology.
1974/75 he was a Sloan Fellow. In 1976 he was awarded the Oswald Veblen - Prize of the American Mathematical Society ( AMS) for his work on foliations. In 1979 he received the Alan T. Waterman Award. In 1978 he gave a plenary lecture at the ICM in Helsinki ( Geometry and Topology in Dimension 3 ) and in 1974 he was invited speaker at the ICM in Vancouver ( On the construction and classification of foliations ). In 2012 he received the Leroy P. Steele Prize. In 2009 he received the first Joseph L. Doob Prize ( for his book Three Dimensional Geometry and Topology ).
Thurston died in August 2012 at the age of 65 from melanoma, which had been diagnosed a year earlier.
Among his doctoral students include Danny Calegari, Richard Canary, David Gabai, Steven Kerckhoff, Yair Minsky, Oded Schramm, Jeffrey Weeks, Richard Kenyon, Silvio Levy, Richard Evan Schwartz, William Goldman (second officer), Benson Farb, William Floyd, Igor Rivin.
Writings
- Three dimensional geometry and topology, Volume 1, Princeton University Press, 1997 ( editor Silvio Levy ), covers only a small part of the lectures at Princeton from 1979 to 1981, the latter are Online
- Hyperbolic structures on 3- manifolds. I. Deformation of acylindrical manifolds, Annals of Mathematics, Volume 124, 1986, pp. 203-246
- Three dimensional manifolds, Kleinian Groups and Hyperbolic Geometry, Bulletin AMS, Volume 6, May 1982, pp. 357-381
- On the geometry and dynamics of diffeomorphisms of surfaces, Bulletin AMS, Volume 19, 1988, pp. 417-431
- Steven Kerckhoff non continuity of the action of the modular group at Bers boundary of Teichmüller space, Inventiones Mathematicae, Volume 100, 1990, pp. 25-47
- With Yakov Eliashberg Confoliations, American Mathematical Society 1998
- Three manifolds, foliations and circles I, Preprint 1997
- Michael Gromov, H. Blaine Lawson Hyperbolic 4- manifolds and conformally flat 3- manifolds, Publications Mathématiques de l' IHES, Vol 68, 1988, pp. 27-45, online
- Existence of codimension one foliations, Annals of Mathematics, Volume 104, 1976, p 249-268
- The theory of foliations of codimension Greater Than one, Comm. Math Helv, Volume 49, 1974, p 214-231
- With David B. Epstein, James W. Cannon, Derek F. Holt, Silvio Levy, Michael S. Paterson Word processing in groups, Jones and Bartlett, Boston 1992
- On proof and progress in mathematics, Bulletin AMS 1994