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Richard Taylor (mathematician)

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Richard Taylor
Taylor in 1999
Born (1962-05-19) 19 May 1962 (age 62)
Cambridge, UK
NationalityBritish, American
Alma materPrinceton University
Clare College, Cambridge
AwardsWhitehead Prize (1990)
Fermat Prize (2001)
Ostrowski Prize (2001)
Cole Prize (2002)
Shaw Prize (2007)
Clay Research Award (2007)
Breakthrough Prize in Mathematics (2014)
Scientific career
FieldsMathematics
InstitutionsInstitute for Advanced Study
Harvard University
Doctoral advisorAndrew Wiles
Doctoral studentsKevin Buzzard
David Geraghty
Elena Mantovan
Sug Woo Shin

Richard Lawrence Taylor (born 19 May 1962) is a British and American[1] mathematician working in the field of number theory.

A former research student of Andrew Wiles, he returned to Princeton to help his advisor complete the proof of Fermat's Last Theorem.

Taylor received the 2014 Breakthrough Prize in Mathematics "for numerous breakthrough results in the theory of automorphic forms, including the Taniyama–Weil conjecture, the local Langlands conjecture for general linear groups, and the Sato–Tate conjecture."[2] He also received the 2007 Shaw Prize in Mathematical Sciences for his work on the Langlands program with Robert Langlands.

Academic career

He received his B.A. from Clare College, Cambridge,[3][4] and his Ph.D. from Princeton University in 1988. From 1995–96 he held the Savilian Chair of Geometry[3] at Oxford University and Fellow of New College, Oxford,[4] and later became the Herchel Smith Professor of Mathematics at Harvard University. He currently works at the Institute for Advanced Study.

He received the Whitehead Prize in 1990, the Fermat Prize, the Ostrowski Prize in 2001, the Cole Prize of the American Mathematical Society in 2002, and the Shaw Prize for Mathematics in 2007. He was also elected a Fellow of the Royal Society in 1995. In 2012 he became a fellow of the American Mathematical Society.[5] In 2015 he was inducted into the National Academy of Sciences.[6]

Work

One of the two papers containing the published proof of Fermat's Last Theorem is a joint work of Taylor and Andrew Wiles.[7]

In subsequent work, Taylor (along with Michael Harris) proved the local Langlands conjectures for GL(n) over a number field.[8] A simpler proof was suggested almost at the same time by Guy Henniart,[9] and ten years later by Peter Scholze.

Taylor, together with Christophe Breuil, Brian Conrad, and Fred Diamond, completed the proof of the Taniyama–Shimura conjecture, by performing quite heavy technical computations in the case of additive reduction.[10]

Recently, Taylor, following the ideas of Michael Harris and building on his joint work with Laurent Clozel, Michael Harris, and Nick Shepherd-Barron, has announced a proof of the Sato–Tate conjecture, for elliptic curves with non-integral j-invariant. This partial proof of the Sato–Tate conjecture uses Wiles's theorem about modularity of semistable elliptic curves.[11]

Personal life

Taylor is the son of British physicist, John C. Taylor. He is married to Christine Taylor (a mathematical biologist). They have two living children: Jeremy and Chloe.[12]

Notes

  1. ^ "Richard L. Taylor".
  2. ^ "Breakthrough Prize". Breakthrough Prize. Retrieved 2014-08-14.
  3. ^ a b SAVILIAN PROFESSORSHIP OF GEOMETRY in NOTICES, University Gazette 23.3.95 No. 4359 [1] Archived October 10, 2007, at the Wayback Machine
  4. ^ a b ‘TAYLOR, Prof. Richard Lawrence’, Who's Who 2008, A & C Black, 2008; online edn, Oxford University Press, Dec 2007 accessed 27 March 2008
  5. ^ List of Fellows of the American Mathematical Society, retrieved 2013-08-25.
  6. ^ National Academy of Sciences Member Directory, retrieved 2016-04-30.
  7. ^ Taylor, R.; Wiles, A. (1995). "Ring theoretic properties of certain Hecke algebras". Ann. of Math. 141 (3): 553–572. doi:10.2307/2118560. {{cite journal}}: Unknown parameter |authormask= ignored (|author-mask= suggested) (help)
  8. ^ Harris, M.; Taylor, R. (2001). The geometry and cohomology of some simple Shimura varieties. Annals of Mathematics Studies. Vol. 151. Princeton University Press. ISBN 0-691-09090-4.
  9. ^ Carayol 1999, pp. 193–194
  10. ^ Breuil, C.; Conrad, B.; Diamond, F.; Taylor, R. (2001). "On the modularity of elliptic curves over Q: wild 3-adic exercises". J. Amer. Math. Soc. 14 (4): 843–939.
  11. ^ Taylor, R. (2008). "Automorphy for some l-adic lifts of automorphic mod l representations. II". Publications Mathématiques de l'IHÉS. 108 (1): 183–239. doi:10.1007/s10240-008-0015-2. {{cite journal}}: Unknown parameter |authormask= ignored (|author-mask= suggested) (help)
  12. ^ Taylor, Richard "The Shaw Prize", 2007

References

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