Vaughan Jones

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
Nationality	New Zealand
Alma mater	University of Geneva University of Auckland
Known for	Von Neumann algebras, knot polynomials, conformal field theory
Awards	Fields Medal (1990)
Scientific career
Fields	Mathematics
Institutions	University of California, Berkeley Vanderbilt University University of California, Los Angeles University of Pennsylvania
Doctoral advisor	André Haefliger

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.

Biography

Vaughan Jones was born in Gisborne, New Zealand and brought up in Cambridge, New Zealand, 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.

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. He remains Professor Emeritus at University of California, Berkeley where he has been on the faculty since 1985 and is a Distinguished Alumni Professor at the University of Auckland.

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

Honours

• 1990 – awarded the Fields Medal.
• 1990 – elected Fellow of the Royal Society.
• 1991 – awarded the Rutherford Medal by the Royal Society of New Zealand.
• 1991 – awarded the degree of Doctor of Science by the University of Auckland
• 1992 – elected to the Australian Academy of Science as a Corresponding Fellow.
• 1992 - awarded a Miller Professorship at the University of California Berkeley.
• 2002 – appointed Distinguished Companion of The New Zealand Order of Merit in the Queen's Birthday Honours 2002, for services to mathematics.
• 2009 – in the Special Honours 2009, redesignated his DCNZM to a Knight Companion of The New Zealand Order of Merit.
• 2012 – became a Fellow of the American Mathematical Society.

Publications

• Jones, Vaughan F.R. (1983). "Index for subfactors". Inventiones Mathematicae. 72 (1): 1–25. 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. 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. MR 0999799.
• 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. MR 1134131.
• 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.

See also

• Jones polynomial
• Aharonov–Jones–Landau algorithm
• Planar algebra
• Subfactor

External links

• O'Connor, John J.; Robertson, Edmund F., "Vaughan Jones", MacTutor History of Mathematics archive, University of St Andrews.
• Vaughan Jones at the Mathematics Genealogy Project
• Jones' home page
• Career profile page at the University of Auckland
• Joan S. Birman: The Work of Vaughan F. R. Jones in Ichirō Satake (ed.): Proceedings of the International Congress of Mathematicians, 21–29 August 1990, Kyoto, Japan, Springer, 1991 (Laudatio for Fields-Medal 1990; online)