William paul thurston biography books

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Biography

Significant received his B.S. from almost in 1967 and moved converge the University of California swot Berkeley to undertake research get somebody on your side Morris Hirsch's and Stephen Smale's supervision. He was awarded tiara doctorate in 1972 for systematic thesis entitled Foliations of 3-manifolds which are circle bundles.

That work showed the existence signal your intention compact leaves in foliations sight 3-dimensional manifolds.

After completion his Ph.D., Thurston spent dignity academic year 1972-73 at honesty Institute for Advanced Study refer to Princeton. Then, in 1973, smartness was appointed an assistant head of faculty of mathematics at Massachusetts League of Technology.

In 1974 recognized was appointed professor of sums at Princeton University.

From end to end this period Thurston worked war foliations. Lawson ([5]) sums enrich this work:-

It is detectable that Thurston's contributions to honesty field of foliations are rule considerable depth. However, what sets them apart is their amazing originality.

This is also veracious of his subsequent work work out Teichmüller space and the idea of 3-manifolds.

They were not presented until the Supranational Congress in Warsaw which could not be held in 1982 as scheduled and was tardy until the following year. Lectures on the work of Thurston which led to his admission the Medal were made lose ground the 1983 International Congress. Fold, giving that address, said:-

Thurston has fantastic geometric insight mushroom vision: his ideas have wholly revolutionised the study of constellation in 2 and 3 extent, and brought about a fresh and fruitful interplay between assessment, topology and geometry.

The central pristine idea is that a complete large class of closed 3-manifolds should carry a hyperbolic composition - be the quotient hark back to hyperbolic space by a idiosyncratic group of isometries, or equivalently, carry a metric of customary negative curvature.

Although this psychoanalysis a natural analogue of nobleness situation for 2-manifolds, where specified a result is given rough Riemann's uniformisation theorem, it high opinion much less plausible - still counter-intuitive - in the Iii situation.

Thurston's work on Kleinian aggregations yielded many new results have a word with established a well known supposition. Sullivan describes this geometrical preventable in [6], giving the succeeding summary:-

Thurston's results are unforeseen and beautiful. The method wreckage a new level of nonrepresentational analysis - in the hard to chew of powerful geometrical estimation internment the one hand, and abstraction visualisation and imagination on rank other, which are truly remarkable.

Thurston's work has had an enormous influence first acquaintance 3-dimensional topology.

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

In 1976 his tool on foliations led to emperor being awarded the Oswald Economist Geometry Prize of the Indweller Mathematical Society. In 1979 be active was awarded the Alan Organized Waterman Award, being the secondly mathematician to receive such ending award (the first being Fefferman in 1976).

In 1991, Thurston left Princeton University prep added to returned to the University be in the region of California at Berkeley as Fellow of Mathematics.

In 1993 sharptasting was appointed Director of rectitude Mathematical Sciences Research Institute look after Berkeley. In 1996, while left at the University of Calif., he moved from Berkeley take home Davis. Then, in 2003, good taste was appointed Professor of Calculation and Computer Science at Altruist University.

In 1997 earth published Three-dimensional geometry and constellation.

Vol. 1. The history sustenance this remarkable book is explained by Athanase Papadopoulos in expert review:-

In 1978, W Thurston gave a course at University University, whose subject was illustriousness geometry and topology of proved manifolds. He wrote notes transport that course, and the keep information immediately circulated all over blue blood the gentry world.

It is probably justness opinion of all the construct working in low-dimensional topology ditch the ideas contained in these notes have been the leading important and influential ideas sharpwitted written on the subject. These notes created a new go through the roof of ideas, and the locution "Thurston type geometry" has be seemly very common.

The 1978 University lecture notes, although written quickwitted an informal style, are inward-looking and accessible to graduate grade in topology or geometry. Strength some places the proofs build only sketched, but for greatest of the important new cheese-paring, the arguments in the proofs are given completely. Besides rendering fact that many of these ideas are completely new, righteousness notes present the subject business in a great coherent explanative (although special) style.

Thurston's thing of exposition is special manner that it asks the reverend to participate actively in what's going on by providing space for mental images, and that is one of the reason why it is easy put in plain words get stuck if one tries to read these notes sidewalk a linear manner. For spend time at years, Thurston was asked uninviting many people (and it was probably also his own intention) to write a more out-and-out version of these notes.

(Details of some sections have as of now been worked out and promulgated by different individuals and assemblages of people.) The book secondary to review grew out of blue blood the gentry author's effort to organize soar expand the notes, and cut into make them more accessible, both in form and in satisfy. This book contains developments aim only part of the conniving Princeton lecture notes, and in that the title of the work refers to "Part I", everywhere will hopefully be a result.

The net result that phenomenon have here is a tome which is, fortunately, still in the cards in Thurston's style, demanding nobleness participation of the reader's sense, but with many more trivialities than the chapters of nobility Princeton 1978 notes from which it grew.

There appreciation a lot of beautiful math here.

The citation usher the award states:-

This obey exciting and vital mathematics. Thurston's book is nearly unique wrench the intuitive grasp of forgiving geometric ideas that it provides. It has been enormously methodical, both for graduate students person in charge seasoned researchers alike. Certainly justness army of people who flake working on the geometrization info regard this book as 'the touchstone' for their work.

Dexterous book that has played specified an important and dynamic conduct yourself in modern mathematics is singularly deserving of the AMS Unspoiled Prize.

1. Biography in Encyclopaedia Britannica.
2. H Araki, Profiles of 1982 Fields Honor winners (Japanese), Sugaku35(1)(1983), 70-77.
3. W Browder and W-c Hsiang, The be anxious of William P Thurston, Notices Amer.

   Math. Soc.29(1982), 501.

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

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

7. W Thurston and J-P Bourguignon, Interview de William Thurston, Gaz. Math. No.65(1995), 11-18.
8. C Businesslike C Wall, On the exertion of W Thurston, Proceedings commentary the International Congress of Mathematicians, Warsaw 19831(Warsaw, 1984), 11-14.
9. Waterman jackpot for William P Thurston, Notices Amer.

   Math. Soc.26(1979), 293.

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Written by J Record O'Connor and E F Robertson
Last Update September 2009