Vaughan Jones

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.

• 1990 – awarded the Fields Medal.
• 1990 – elected Fellow of the Royal Society.[5]
• 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 (DCNZM) in the 2002 Queen’s Birthday and Golden Jubilee Honours, for services to mathematics.[6]
• 2009 – redesignated his DCNZM to a Knight Companion of the New Zealand Order of Merit in the 2009 Special Honours.[7]
• 2012 – elected a Fellow of the American Mathematical Society.[8]

• 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.

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

Wikimedia Commons has media related to Vaughan Jones.

• 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)