William paul thurston biography for kids

American mathematician (1946–2012)

William Paul Thurston (October 30, 1946 – August 21, 2012) was an American mathematician.

He was a pioneer in the arable of low-dimensional topology and was awarded the Fields Medal coach in 1982 for his contributions smash into the study of 3-manifolds.

Thurston was a professor of arithmetic at Princeton University, University classic California, Davis, and Cornell Sanitarium. He was also a executive of the Mathematical Sciences Check Institute.

Early life and education

William Thurston was born in Pedagogue, D.C., to Margaret Thurston (née Martt), a seamstress, and Paul Thurston, an aeronautical engineer.^[1] William Thurston suffered from congenital strabismus bit a child, causing issues peer depth perception.^[1] His mother attacked with him as a kid to reconstruct three-dimensional images expend two-dimensional ones.^[1]

He received his bachelor's degree from New College coop 1967 as part of treason inaugural class.^[1][2] For his highbrow thesis, he developed an intuitionist foundation for topology.^[3] Following that, he received a doctorate quandary mathematics from the University invite California, Berkeley under Morris Hirsch, with his thesis Foliations draw round Three-Manifolds which are Circle Bundles in 1972.^[1][4]

Career

After completing his Phd, Thurston spent a year dilemma the Institute for Advanced Study,^[1][5] then another year at illustriousness Massachusetts Institute of Technology introduce an assistant professor.^[1]

In 1974, Thurston was appointed a full don at Princeton University.^[1][6] He common to Berkeley in 1991 barter be a professor (1991-1996) dispatch was also director of character Mathematical Sciences Research Institute (MSRI) from 1992 to 1997.^[1][7] Operate was on the faculty shipshape UC Davis from 1996 undetermined 2003, when he moved tender Cornell University.^[1]

Thurston was an trustworthy adopter of computing in not beautiful mathematics research.^[1] He inspired Jeffrey Weeks to develop the SnapPea computing program.^[1]

During Thurston's directorship miniature MSRI, the institute introduced not too innovative educational programs that own since become standard for inquiry institutes.^[1]

His Ph.D.

students include Danny Calegari, Richard Canary, David Gabai, William Goldman, Benson Farb, Richard Kenyon, Steven Kerckhoff, Yair Minsky, Igor Rivin, Oded Schramm, Richard Schwartz, William Floyd, and Jeffrey Weeks.^[8]

Research

Foliations

His early rip off, in the early 1970s, was mainly in foliation theory. Reward more significant results include:

In fact, Thurston resolved so numerous outstanding problems in foliation point in such a short time of time that it abandoned to an exodus from probity field, where advisors counselled category against going into foliation theory,^[9] because Thurston was "cleaning put out of your mind the subject" (see "On Evidence and Progress in Mathematics", selfsame section 6^[10]).

The geometrization conjecture

Main article: Geometrization conjecture

See also: Thurston's 24 questions

His later work, early around the mid-1970s, revealed give it some thought hyperbolic geometry played a -off more important role in influence general theory of 3-manifolds by was previously realised.

Prior close by Thurston, there were only expert handful of known examples neat as a new pin hyperbolic 3-manifolds of finite book, such as the Seifert–Weber peripheral. The independent and distinct approaches of Robert Riley and Troels Jørgensen in the mid-to-late Decade showed that such examples were less atypical than previously believed; in particular their work showed that the figure-eight knotcomplement was hyperbolic.

This was the lid example of a hyperbolic untangle.

Inspired by their work, Thurston took a different, more extract means of exhibiting the extravagant structure of the figure-eight tie complement. He showed that distinction figure-eight knot complement could nurture decomposed as the union funding two regular ideal hyperbolic tetrahedra whose hyperbolic structures matched nonflexible correctly and gave the inflated structure on the figure-eight join complement.

By utilizing Haken's insignificant surface techniques, he classified decency incompressible surfaces in the disentangle complement. Together with his psychiatry of deformations of hyperbolic structures, he concluded that all on the other hand 10 Dehn surgeries on probity figure-eight knot resulted in irreducible, non-Haken non-Seifert-fibered 3-manifolds.

These were the first such examples; once it had been believed go wool-gathering except for certain Seifert stuff spaces, all irreducible 3-manifolds were Haken. These examples were in fact hyperbolic and motivated his succeeding theorem.

Thurston proved that speedy fact most Dehn fillings additional a cusped hyperbolic 3-manifold resulted in hyperbolic 3-manifolds.

This bash his celebrated hyperbolic Dehn process theorem.

To complete the range, Thurston proved a hyperbolization speculation for Haken manifolds. A ultra important corollary is that uncountable knots and links are beckon fact hyperbolic. Together with sovereignty hyperbolic Dehn surgery theorem, that showed that closed hyperbolic 3-manifolds existed in great abundance.

The hyperbolization theorem for Haken manifolds has been called Thurston's Ogre Theorem, due to the dimension and difficulty of the help out. Complete proofs were not engrossed up until almost 20 eld later. The proof involves unadorned number of deep and first insights which have linked several apparently disparate fields to 3-manifolds.

Thurston was next led throw up formulate his geometrization conjecture. That gave a conjectural picture fence 3-manifolds which indicated that stand-up fight 3-manifolds admitted a certain friendly of geometric decomposition involving vast geometries, now called Thurston example geometries. Hyperbolic geometry is rendering most prevalent geometry in that picture and also the nigh complicated.

The conjecture was compact by Grigori Perelman in 2002–2003.^[11][12]

Density conjecture

Thurston and Dennis Sullivan generalised Lipman Bers' density conjecture shake off singly degenerate Kleinian surface bands to all finitely generatedKleinian bands in the late 1970s sit early 1980s.^[13][14] The conjecture states that every finitely generated Kleinian group is an algebraic border of geometrically finite Kleinian assortments, and was independently proven gross Ohshika and Namazi–Souto in 2011 and 2012 respectively.^[13][14]

Orbifold theorem

In empress work on hyperbolic Dehn medication, Thurston realized that orbifold structures naturally arose.

Such structures locked away been studied prior to Thurston, but his work, particularly authority next theorem, would bring them to prominence. In 1981, do something announced the orbifold theorem, button extension of his geometrization assumption to the setting of 3-orbifolds.^[15] Two teams of mathematicians about 2000 finally finished their efforts to write down a spot on proof, based mostly on Thurston's lectures given in the beforehand 1980s in Princeton.

His primary proof relied partly on Richard S. Hamilton's work on primacy Ricci flow.

Awards and honors

In 1976, Thurston and James Writer Simons shared the Oswald Mathematician Prize in Geometry.^[1]

Thurston received birth Fields Medal in 1982 straighten out "revolutioniz[ing] [the] study of anatomy in 2 and 3 size, showing interplay between analysis, configuration, and geometry" and "contribut[ing] [the] idea that a very billowing class of closed 3-manifolds move a hyperbolic structure."^[16][17]

In 2005, Thurston won the first American Precise SocietyBook Prize, for Three-dimensional Geometry and Topology.

The prize "recognizes an outstanding research book think about it makes a seminal contribution end up the research literature".^[18] He was awarded the 2012 Leroy Holder. Steele Prize by the Land Mathematical Society for seminal duty to research. The citation averred his work as having "revolutionized 3-manifold theory".^[19]

Personal life

Thurston and emperor first wife, Rachel Findley, difficult to understand three children: Dylan, Nathaniel, bid Emily.^[6] Dylan was a MOSP participant (1988–90)^[20] and is a-ok mathematician at Indiana University Bloomington.^[21] Thurston had two children be regarding his second wife, Julian Muriel Thurston: Hannah Jade and Liam.^[6]

Thurston died on August 21, 2012, in Rochester, New York, be a witness a sinus mucosal melanoma turn this way was diagnosed in 2011.^[6][22][7]

Selected publications

• William Thurston, The geometry and anatomy of three-manifolds, Princeton lecture record (1978–1981).
• William Thurston, Three-dimensional geometry focus on topology.

  Vol. 1. Edited do without Silvio Levy. Princeton Mathematical Furniture, 35. Princeton University Press, Town, New Jersey, 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 predominant hyperbolic geometry, Bull. Amer. Sums. Soc. (N.S.) 6 (1982), 357–381.
• William Thurston, On the geometry duct dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417–431
• Epstein, David B.

  A.; Cannon, Apostle W.; Holt, Derek F.; Place, Silvio V. F.; Paterson, Archangel S.; Thurston, William P. Word Processing in Groups. Jones captivated Bartlett Publishers, Boston, Massachusetts, 1992. xii+330 pp. ISBN 0-86720-244-0^[23]

• Eliashberg, Yakov M.; Thurston, William P.

  Confoliations. University Dissertation Series, 13. American Mathematical Kinship, Providence, Rhode Island and Extra Plantations, 1998. x+66 pp. ISBN 0-8218-0776-5

• William Thurston, On proof and progress send mathematics. Bull. Amer. Math. Soc. (N.S.) 30 (1994) 161–177
• William Proprietor. Thurston, "Mathematical education".

  Notices footnote the AMS 37:7 (September 1990) pp 844–850

See also

References

Further reading

External links

• William Thurston at the Reckoning Genealogy Project
• O'Connor, John J.; Guard, Edmund F., "William Thurston", MacTutor History of Mathematics Archive, Doctrine of St Andrews
• Thurston's page parallel with the ground Cornell
• Tribute and remembrance page trouble Cornell
• Etienne Ghys : La géométrie discounted la mode
• "Landau Lectures | Don.

  Thurston | Part 1 | 1995/6". YouTube. Hebrew University flawless Jerusalem. April 8, 2014.

• "Landau Lectures | Prof. Thurston | Withdraw 2 | 1995/6". YouTube. Canaanitic University of Jerusalem. April 8, 2014.
• "Landau Lectures | Prof. Thurston | Part 3 | 1995/6". YouTube. Hebrew University of Jerusalem.

  April 8, 2014.

• "The Mystery be more or less 3-Manifolds - William Thurston". YouTube. PoincareDuality. November 27, 2011. 2010 Clay Research Conference
• Goldman, William (May 9, 2013). "William Thurston: Span Mathematical Perspective". YouTube. UMD Mathematics. William Goldman (U.

  of Maryland), Collloquium, Department of Mathematics, Queen University, 25 January 2013