William Thurston
In his work on hyperbolic Dehn surgery, Thurston realized that orbifold structures naturally arose. Such structures had been studied prior to Thurston, but his work, particularly the next theorem, would bring them to prominence. In 1981, he announced the orbifold theorem, an extension of his geometrization theorem to the setting of 3-orbifolds. Two teams of mathematicians around 2000 finally finished their efforts to write down a complete proof, based mostly on Thurston's lectures given in the early 1980s in Princeton. His original proof relied partly on Hamilton's work on the Ricci flow.
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Education and career
He was born in Washington, D.C and received his bachelors degree from New College (now New College of Florida) in 1967. For his undergraduate thesis he developed an intuitionist foundation for topology. Following this, he earned a doctorate in mathematics from the University of California, Berkeley, in 1972. His Ph.D. advisor was Morris W. Hirsch and his dissertation was on Foliations of Three-Manifolds which are Circle Bundles.
After completing his Ph.D., he spent a year at the Institute for Advanced Study, then another year at MIT as Assistant Professor. In 1974, he was appointed Professor of Mathematics at Princeton University. In 1991, he returned to UC-Berkeley as Professor of Mathematics and in 1993 became Director of the Mathematical Sciences Research Institute. In 1996, he moved to University of California, Davis. In 2003, he moved again to become Professor of Mathematics at Cornell University.
His Ph.D. students include Richard Canary, David Gabai, William Goldman, Benson Farb, Detlef Hardorp, Craig Hodgson, Steven Kerckhoff, Robert Meyerhoff, Yair Minsky, Lee Mosher, Igor Rivin, Oded Schramm, Richard Schwartz, Martin Bridgeman and Jeffrey Weeks.
Thurston has turned his attention in recent years to mathematical education and bringing mathematics to the general public. He has served as mathematics editor for Quantum Magazine, a youth science magazine, and as head of The Geometry Center. As director of Mathematical Sciences Research Institute from 1992 to 1997, he initiated a number of programs designed to increase awareness of mathematics among the public.
In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature.[2]
Thurston has an Erdős number of 2.
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Selected works
- William Thurston, The geometry and topology of 3-manifolds, Princeton lecture notes (1978-1981).
- William Thurston. Three-dimensional geometry and topology. Vol. 1. Edited by Silvio Levy. Princeton Mathematical Series, 35. Princeton University Press, Princeton, NJ, 1997. x+311 pp. ISBN 0-691-08304-5
- William Thurston, Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds. Ann. of Math. (2) 124 (1986), no. 2, 203--246.
- William Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 357–381.
- William Thurston. On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417--431
- Epstein, David B. A.; Cannon, James W.; Holt, Derek F.; Levy, Silvio V. F.; Paterson, Michael S.; Thurston, William P. Word processing in groups. Jones and Bartlett Publishers, Boston, MA, 1992. xii+330 pp. ISBN 0-86720-244-0
- Eliashberg, Yakov M.; Thurston, William P. Confoliations. University Lecture Series, 13. American Mathematical Society, Providence, RI, 1998. x+66 pp. ISBN 0-8218-0776-5
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See also
- Milnor–Thurston kneading theory
- Nielsen-Thurston classification
- Jorgensen-Thurston theorem
- confoliation
- automatic group
- Thurston norm
- Geometrization
- Geometric structure
- Circle packing theorem
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External links
- William Thurston at the Mathematics Genealogy Project
- O'Connor, John J. & Robertson, Edmund F., “William Thurston”, MacTutor History of Mathematics archive
- Thurston's page at Cornell
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