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| Thurston, William P. | |
|---|---|
| Name | William P. Thurston |
| Birth date | 1946-10-30 |
| Death date | 2012-08-21 |
| Nationality | American |
| Fields | Topology, Geometry |
| Workplaces | Princeton University, University of California, Berkeley, Stony Brook University |
| Alma mater | University of California, Berkeley, University of California, Los Angeles |
| Doctoral advisor | William Browder |
Thurston, William P. William Paul Thurston was an American mathematician noted for transformative work in low-dimensional topology, hyperbolic geometry, and the theory of foliations. His insights reshaped research at institutions such as Princeton University, University of California, Berkeley, and Stony Brook University, influencing contemporaries including Dennis Sullivan, Edward Witten, and Michael Freedman. Thurston's 1970s and 1980s contributions established deep links between Kleinian groups, Teichmüller theory, and three-dimensional manifold topology, culminating in conjectures and theorems that guided later work by researchers like Grigori Perelman.
Thurston was born in Washington and raised partly in California. He completed undergraduate studies at the University of California, Berkeley and earned a Ph.D. from the University of California, Los Angeles under advisor William Browder. During graduate training he was in contact with figures from the Princeton University and Institute for Advanced Study circles, absorbing ideas from scholars such as John Milnor and Shing-Tung Yau. Early influences included classical work by Henri Poincaré, the development of knot theory by Thurston's predecessors, and modern approaches to foliations by Charles Ehresmann and Georges Reeb.
Thurston introduced revolutionary concepts to three-dimensional manifold topology, formulating the Geometrization conjecture that proposed a canonical decomposition of 3-manifolds into pieces with homogeneous geometries related to the eight Thurston geometries, connecting to work of Bernhard Riemann and Élie Cartan. He proved hyperbolization results for Haken manifolds and developed a theory of hyperbolic structures on 3-manifolds that interacted with the study of Kleinian group dynamics, building on foundations by Ahlfors and Ahlfors's contemporaries. Thurston's introduction of measured laminations and the Thurston compactification of Teichmüller space provided tools later employed by William Goldman, Curtis McMullen, and Howard Masur. His work on pseudo-Anosov diffeomorphisms and the classification of surface homeomorphisms extended concepts from Henri Poincaré and influenced Maryam Mirzakhani's later research. Thurston's insights into circle packing and discrete conformal structures influenced computational approaches adopted by Ken Stephenson and integrated with classical results from Gauss and Riemann. The interplay between Thurston's conjectures and the eventual proofs by Grigori Perelman of the Poincaré conjecture highlighted connections to Richard Hamilton's Ricci flow program and the broader work of Michael Freedman on four-manifolds.
Thurston held faculty positions at Princeton University, University of California, Berkeley, and Cornell University, and later at Stony Brook University, where he taught graduate and undergraduate courses that emphasized geometric intuition and topological visualization. His students and collaborators included R. C. Penner, John H. Conway's circle of geometers, and others who became prominent in geometric group theory and dynamical systems, such as Richard Canary and Oded Schramm. Thurston championed expository clarity in lectures and notes, influencing pedagogical practices at the Institute for Advanced Study and informing curricula at the Courant Institute of Mathematical Sciences. He organized workshops and lecture series that brought together researchers from Kleinian group theory, Teichmüller theory, and computational geometry, fostering collaborations with scholars affiliated with Brown University, Harvard University, and the University of Chicago.
Thurston received numerous accolades, including the Fields Medal in 1982 for his contributions to topology and geometry, the National Medal of Science from the United States government, and election to the National Academy of Sciences. He held memberships in learned societies such as the American Academy of Arts and Sciences and delivered major lectures like the International Congress of Mathematicians plenary address. His recognition paralleled awards given to contemporaries such as Simon Donaldson and Michael Atiyah, and he shared platforms with laureates like Edward Witten and Alain Connes.
Thurston authored influential writings ranging from lecture notes to formal articles, including "The Geometry and Topology of Three-Manifolds," extensive seminar notes that circulated widely among researchers and students and influenced work by William Goldman and Curtis McMullen. Other key publications addressed circle packing, measured laminations, and the classification of surface diffeomorphisms, intersecting with literature by Masur, N. V. Ivanov, and John Harer. His expository articles appeared in venues associated with the American Mathematical Society and collections honoring figures like Raoul Bott and Lars Hörmander.
In later years Thurston continued to write and lecture, addressing topics from mathematical visualization to the foundations of geometry; his outreach influenced software development in computational topology produced by teams at Geometry Center and academic labs at Brown University and Stanford University. The proof of the Geometrization conjecture via Ricci flow and Perelman's work confirmed many of Thurston's predictions and cemented his status among canonical figures such as Henri Poincaré and Bernhard Riemann. His ideas persist across active research areas including geometric group theory, Kleinian group dynamics, and low-dimensional topology, and his students and collaborators maintain vibrant lines of inquiry at institutions like Princeton University, Stony Brook University, and the Institute for Advanced Study.
Category:American mathematicians Category:Topologists Category:Fields Medalists