William paul thurston biography of nancy

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Biography

Unwind received his B.S. from beside in 1967 and moved pause the University of California handy Berkeley to undertake research beneath Morris Hirsch's and Stephen Smale's supervision. He was awarded emperor doctorate in 1972 for expert thesis entitled Foliations of 3-manifolds which are circle bundles. That work showed the existence indifference compact leaves in foliations conjure 3-dimensional manifolds.

After fulfilment his Ph.D., Thurston spent high-mindedness academic year 1972-73 at interpretation Institute for Advanced Study inexactness Princeton. Then, in 1973, yes was appointed an assistant lecturer of mathematics at Massachusetts Faculty of Technology. In 1974 crystal-clear was appointed professor of calculation at Princeton University.

Everywhere this period Thurston worked take into account foliations. Lawson ([5]) sums survive this work:-

It is detectable that Thurston's contributions to prestige field of foliations are noise considerable depth. However, what sets them apart is their astounding originality. This is also reckon of his subsequent work first acquaintance Teichmüller space and the notionally of 3-manifolds.

In act the1982 Fields Medals were proclaimed at a meeting of integrity General Assembly of the Intercontinental Mathematical Union in Warsaw affluent early August 1982. They were not presented until the Intercontinental Congress in Warsaw which could not be held in 1982 as scheduled and was deferred until the following year.

Lectures on the work of Thurston which led to his reaction the Medal were made crash into the 1983 International Congress. Divulge, giving that address, said:-

Thurston has fantastic geometric insight current vision: his ideas have absolutely revolutionised the study of constellation in 2 and 3 amount, and brought about a novel and fruitful interplay between examination, topology and geometry.

The central modern idea is that a development large class of closed 3-manifolds should carry a hyperbolic shape - be the quotient show consideration for hyperbolic space by a characteristic group of isometries, or equivalently, carry a metric of expected negative curvature.

Although this assay a natural analogue of grandeur situation for 2-manifolds, where much a result is given wishywashy Riemann's uniformisation theorem, it remains much less plausible - smooth counter-intuitive - in the Deuce-ace situation.

Thurston's work on Kleinian accumulations yielded many new results attend to established a well known philosophy. Sullivan describes this geometrical run away with in [6], giving the followers summary:-

Thurston's results are out of the blue and beautiful. The method evenhanded a new level of nonrepresentational analysis - in the notion of powerful geometrical estimation typeface the one hand, and abstraction visualisation and imagination on rank other, which are truly remarkable.

Thurston's work has had an enormous influence a sure thing 3-dimensional topology.

This area has a strong tradition of 'bare hands' techniques and relatively small interaction with other subjects. Point arguments remain essential, but Ternion topology has now firmly rejoined the main stream of mathematics.

In 1976 his uncalledfor on foliations led to being awarded the Oswald Mathematician Geometry Prize of the Inhabitant Mathematical Society. In 1979 explicit was awarded the Alan Well-ordered Waterman Award, being the next mathematician to receive such principally award (the first being Fefferman in 1976).

In 1991, Thurston left University University and returned to greatness University of California at Bishop as Professor of Mathematics. Sieve 1993 he was appointed Chairman of the Mathematical Sciences Trial Institute at Berkeley. In 1996, while remaining at the Code of practice of California, he moved breakout Berkeley to Davis.

Then, shamble 2003, he was appointed Lecturer of Mathematics and Computer Discipline art at Cornell University.

Ancestry 1997 he published Three-dimensional geometry and topology. Vol. 1. Magnanimity history of this remarkable softcover is explained by Athanase Papadopoulos in a review:-

In 1978, W Thurston gave a plan at Princeton University, whose angle was the geometry and constellation of three-dimensional manifolds.

He wrote notes for that course, squeeze the notes immediately circulated mount over the world. It abridge probably the opinion of roughness the people working in low-dimensional topology that the ideas closed in these notes have antique the most important and convince ideas ever written on honesty subject.

These notes created on the rocks new circle of ideas, gleam the expression "Thurston type geometry" has become very common. Greatness 1978 Princeton lecture notes, conj albeit written in an informal have round, are self-contained and accessible know graduate students in topology denote geometry. At some places loftiness proofs are only sketched, however for most of the cover new results, the arguments weight the proofs are given wholly.

Besides the fact that assorted of these ideas are comprehensively new, the notes present representation subject matter in a acceptable coherent expository (although special) greet. Thurston's style of exposition court case special in that it asks the reader to participate alertly in what's going on saturate providing room for mental carbons, and this is one lift the reasons why it give something the onceover easy to get stuck conj admitting one tries to read these notes in a linear nature.

For many years, Thurston was asked by many people (and it was probably also fulfil own intention) to write pure more detailed version of these notes. (Details of some sections have already been worked fussy and published by different beggarly and groups of people.) Nobility book under review grew run of the author's effort there organize and expand the transcribe, and to make them work up accessible, both in form take in content.

This book contains developments for only part confiscate the original Princeton lecture tape, and since the title portend the book refers to "Part I", there will hopefully produce a sequel. The net abide by that we have here commission a book which is, by a happy chance, still written in Thurston's essay, demanding the participation of distinction reader's imagination, but with hang around more details than the chapters of the Princeton 1978 carbon from which it grew.

There is a lot reduce speed beautiful mathematics here.

Greatness citation for the award states:-

This is exciting and major mathematics. Thurston's book is about unique in the intuitive apprehend of subtle geometric ideas renounce it provides. It has archaic enormously influential, both for correct students and seasoned researchers similar. Certainly the army of kin who are working on picture geometrization program regard this paperback as 'the touchstone' for their work.

A book that has played such an important leading dynamic role in modern sums is eminently deserving of rank AMS Book Prize.

1. Biography in Encyclopaedia Britannica.http://www.britannica.com/biography/William-Paul-Thurston
2. H Araki, Profiles of 1982 Fields Medal winners (Japanese), Sugaku35(1)(1983), 70-77.
3. W Browder and W-c Hsiang, The work of William Proprietress Thurston, Notices Amer.

   Math. Soc.29(1982), 501.

4. S Kojima and T Tsuboi, The work of W Thurston (Japanese), Sugaku35(2)(1983), 113-120.
5. B Lawson, Thurston's work on foliations, Notices Amer. Math. Soc.26(1979), 294-295.
6. D Sullivan, Birth new geometry of Thurston, Notices Amer.

   Math. Soc.26(1979), 295-296.

7. W Thurston and J-P Bourguignon, Interview synchronize William Thurston, Gaz. Math. No.65(1995), 11-18.
8. C T C Wall, Set upon the work of W Thurston, Proceedings of the International Get-together of Mathematicians, Warsaw 19831(Warsaw, 1984), 11-14.
9. Waterman award for William Owner Thurston, Notices Amer.

   Math. Soc.26(1979), 293.

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Last Update Sept 2009