Richard Taylor (mathematician)

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Richard Taylor (born Richard Lawrence Taylor 19 May 1962) is a British 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 2007 Shaw Prize in Mathematical Sciences for his work on the Langlands program with Robert Langlands.

Academic career

He received his Ph.D. from Princeton University in 1988. From 1995 to 1996 he held the Savilian Chair of Geometry at Oxford University and Fellow of New College, Oxford [‘TAYLOR, Prof. Richard Lawrence’, Who's Who 2008, A & C Black, 2008; online edn, Oxford University Press, Dec 2007 [http://www.ukwhoswho.com/view/article/oupww/whoswho/U37171, accessed 27 March 2008] ] , and he is currently the Herchel Smith Professor of Mathematics at Harvard University.

He received the Whitehead Prize in 1990, the Fermat Prize and the Ostrowski Prize in 2001 andthe Cole Prize of the American Mathematical Society in 2002. He was also elected a Fellow of the Royal Society in 1995.

Work

One of the two papers containing the published proof of Fermat's Last Theorem is a joint work of Taylor and Andrew Wiles. [R. Taylor and A. Wiles, " [http://dx.doi.org/10.2307/2118560 Ring theoretic properties of certain Hecke algebras] ", Ann. of Math. 141 (1995), no. 3, pp. 553-572 (subscription required to view article)]

In subsequent work, Taylor (along with Michael Harris) proved the local Langlands conjectures for GL("n") over a number field. [M. Harris and R. Taylor, "The geometry and cohomology of some simple Shimura varieties", Annals of Mathematics Studies, no. 151, Princeton University Press, 2001. ISBN 0-691-09090-4]

Taylor, along with Christophe Breuil, Brian Conrad, and Fred Diamond, completed the proof of the Taniyama-Shimura conjecture. [C. Breuil, B. Conrad, F. Diamond and R. Taylor, "On the modularity of elliptic curves over" Q ": wild 3-adic exercises", J. Amer. Math. Soc. 14 (2001), no. 4, pp. 843-939]

Very recently, Taylor, building on his own work and that of 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 follows from a modularity result, generalizing Wiles's result for elliptic curves. [R. Taylor, " Automorphy for some l-adic lifts of automorphic mod l representations. II", preprint available at his [http://www.math.harvard.edu/~rtaylor/ website] .]

Some expert opinion now predicts that the removal of the technical condition, and the full Sato-Tate conjecture, will follow from the stabilization of the Selberg trace formula. That is, Sato-Tate is rumoured now to be subject to a conditional proof.

Personal life

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

External links

* [http://www.math.harvard.edu/~rtaylor/ His home page at Harvard]
* [http://www.math.columbia.edu/~goldfeld/Taylor.pdf Undated PDF talk summary apparently by Taylor]

References