Vaughan Jones

Sir Vaughan Frederick Randal Jones KNZM FRS FRSNZ FAA (born 31 December 1952) is a New Zealand mathematician, known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990, and famously wore a New Zealand rugby jersey when he gave his acceptance speech in Kyoto.

This article is about the mathematician. For the former soccer player, see Vaughan Jones (footballer).

Sir Vaughan Jones

KNZM FRS FRSNZ FAA
Vaughan Jones in 2007
Born
Vaughan Frederick Randal Jones

(1952-12-31) 31 December 1952
Gisborne, New Zealand
NationalityNew Zealand
Alma materUniversity of Geneva
University of Auckland
Known forVon Neumann algebras, knot polynomials, conformal field theory
AwardsFields Medal (1990)
Scientific career
FieldsMathematics
InstitutionsUniversity of California, Berkeley
Vanderbilt University
University of California, Los Angeles
University of Pennsylvania
Doctoral advisorAndré Haefliger

Biography

Vaughan Jones was born in Gisborne, New Zealand and brought up in Cambridge, New Zealand. He attended St Peter's School, before completing secondary school at Auckland Grammar School. His undergraduate studies were at the University of Auckland, from where he obtained a BSc in 1972 and an MSc in 1973. For his graduate studies, he went to Switzerland, where he completed his PhD at the University of Geneva in 1979. His thesis, titled Actions of finite groups on the hyperfinite II1 factor, was written under the supervision of André Haefliger. In 1980, he moved to the United States, where he taught at the University of California, Los Angeles (1980–1981) and the University of Pennsylvania (1981–1985), before being appointed as Professor of Mathematics at the University of California, Berkeley.[1]

His work on knot polynomials, with the discovery of what is now called the Jones polynomial, was from an unexpected direction with origins in the theory of von Neumann algebras, an area of analysis already much developed by Alain Connes. It led to the solution of a number of classical problems of knot theory, and to increased interest in low-dimensional topology.

Jones has since 2011 been at Vanderbilt University as Stevenson Distinguished Professor of mathematics.[2] He remains Professor Emeritus at University of California, Berkeley where he has been on the faculty since 1985[3] and is a Distinguished Alumni Professor at the University of Auckland.[4]

He was made an honorary vice-president for life of the International Guild of Knot Tyers in 1992.

Honours and awards

Publications
  • Jones, Vaughan F.R. (1983). "Index for subfactors". Inventiones Mathematicae. 72 (1): 1–25. Bibcode:1983InMat..72....1J. doi:10.1007/BF01389127. MR 0696688.
  • Jones, Vaughan F.R. (1985). "A polynomial invariant for knots via von Neumann algebra". Bulletin of the American Mathematical Society. (N.S.). 12: 103–111. doi:10.1090/s0273-0979-1985-15304-2. MR 0766964.
  • Jones, Vaughan F.R. (1987). "Hecke algebra representations of braid groups and link polynomials". Annals of Mathematics. (2). 126 (2): 335–388. doi:10.2307/1971403. JSTOR 1971403. MR 0908150.
  • Jones, Vaughan F.R. (1980). Actions of finite groups on the hyperfinite type II1 factor. Memoirs of the American Mathematical Society.
  • Goodman, Frederick M.; de la Harpe, Pierre; Jones, Vaughan F.R. (1989). Coxeter graphs and towers of algebras. Mathematical Sciences Research Institute Publications. 14. Springer-Verlag. doi:10.1007/978-1-4613-9641-3. ISBN 978-1-4613-9643-7. MR 0999799.[9]
  • Jones, Vaughan F.R. (1991). Subfactors and knots. CBMS Regional Conference Series in Mathematics. 80. Providence, RI: American Mathematical Society. doi:10.1090/cbms/080. ISBN 9780821807293. MR 1134131.[10]
  • Jones, Vaughan F.R.; Sunder, Viakalathur Shankar (1997). Introduction to subfactors. London Mathematical Society Lecture Note Series. 234. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511566219. ISBN 0-521-58420-5. MR 1473221.
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See also

References
  1. Lambert, Max; Traue, James Edward; Taylor, Alister (1991). Who's Who in New Zealand, 1991 (12th ed.). Auckland: Octopus. p. 331. Retrieved 29 July 2015.
  2. Personal web page at Vanderbilt University
  3. Personal web page at Berkeley
  4. Personal web page at Auckland
  5. "Fellows". Royal Society. Retrieved 5 November 2010.
  6. "Queen's Birthday and Golden Jubilee honours list 2002". Department of the Prime Minister and Cabinet. 3 June 2002. Retrieved 25 June 2020.
  7. "Special honours list 1 August 2009". Department of the Prime Minister and Cabinet. 5 April 2011. Retrieved 25 June 2020.
  8. List of Fellows of the American Mathematical Society, retrieved 26 January 2013.
  9. Birman, Joan S. (1991). "Review: Coxeter graphs and towers of algebras, by F. M. Goodman, P. de la Harpe, and V. F. R. Jones". Bulletin of the American Mathematical Society. (N.S.). 25 (1): 195–199. doi:10.1090/s0273-0979-1991-16063-5.
  10. Kauffman, Louis H. (1994). "Review: Subfactors and knots, by V. F. R. Jones". Bulletin of the American Mathematical Society. (N.S.). 31 (1): 147–154. doi:10.1090/s0273-0979-1994-00509-9.
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