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Sir Vaughan Jones | |
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Vaughan Jones in 2007 | |

Born | Vaughan Frederick Randal Jones 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.

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 II _{1} 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.^{ [1] } He remains Professor Emeritus at University of California, Berkeley where he has been on the faculty since 1985^{ [2] } and is a Distinguished Alumni Professor at the University of Auckland.^{ [3] }

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.
^{ [4] } - 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.
^{ [5] } - 2009 –in the Special Honours 2009, redesignated his DCNZM to a Knight Companion of The New Zealand Order of Merit.
^{ [6] } - 2012 –became a Fellow of the American Mathematical Society.
^{ [7] }

- 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 II*. Memoirs of the American Mathematical Society._{1}factor - 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.^{ [8] } - 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.^{ [9] } - 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.

**Oscar Zariski** was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century.

In the mathematical field of knot theory, the **Jones polynomial** is a knot polynomial discovered by Vaughan Jones in 1984.,. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable with integer coefficients.

**Richard Peter Stanley** is an Emeritus Professor of Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. From 2000 to 2010, he was the Norman Levinson Professor of Applied Mathematics. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is an expert in the field of combinatorics and its applications to other mathematical disciplines.

In mathematics, **planar algebras** first appeared in the work of Vaughan Jones on the standard invariant of a II_{1} subfactor. They also provide an appropriate algebraic framework for many knot invariants (in particular the Jones polynomial), and have been used in describing the properties of Khovanov homology with respect to tangle composition. Any subfactor planar algebra provides a family of unitary representations of Thompson groups. Any finite group (and quantum generalization) can be encoded as a planar algebra.

In the theory of von Neumann algebras, a **subfactor** of a factor is a subalgebra that is a factor and contains . The theory of subfactors led to the discovery of the Jones polynomial in knot theory.

**Ian Grant Macdonald** is a British mathematician known for his contributions to symmetric functions, special functions, Lie algebra theory and other aspects of algebra, algebraic combinatorics, and combinatorics.

**David Eisenbud** is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and was Director of the Mathematical Sciences Research Institute (MSRI) from 1997 to 2007. He was reappointed to this office in 2013, and his term has been extended until July 31, 2022.

**Phillip Augustus Griffiths IV** is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory. He also worked on partial differential equations, coauthored with Chern, Robert Bryant and Robert Gardner on Exterior Differential Systems.

**Robert Vaughan Moody**, is a Canadian mathematician. He is the co-discover of Kac–Moody algebra, a Lie algebra, usually infinite-dimensional, that can be defined through a generalized root system.

**Igor Borisovich Frenkel** is a Russian-American mathematician at Yale University working in representation theory and mathematical physics.

**William Bernard Raymond Lickorish** is a mathematician. He is emeritus professor of geometric topology in the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, and also an emeritus fellow of Pembroke College, Cambridge. His research interests include topology and knot theory. He was one of the discoverers of the HOMFLY polynomial invariant of links, and proved the Lickorish-Wallace theorem which states that all closed orientable 3-manifolds can be obtained by Dehn surgery on a link.

**János Kollár** is a Hungarian mathematician, specializing in algebraic geometry.

**Charles Whittlesey Curtis** is a mathematician and historian of mathematics, known for his work in finite group theory and representation theory. He is a retired professor of mathematics at the University of Oregon.

**Claudio Procesi** is an Italian mathematician, known for works in algebra and representation theory.

**Tsit Yuen Lam** is a Hong Kong-American mathematician specializing in algebra, especially ring theory and quadratic forms.

**Nolan Russell Wallach** is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the 2-volume treatise *Real Reductive Groups*.

**Kenneth C. Millett** is a professor of mathematics at the University of California, Santa Barbara. His research concerns low-dimensional topology, knot theory, and the applications of knot theory to DNA structure; his initial is the "M" in the name of the HOMFLY polynomial.

**Stephen Carl Milne** is an American mathematician who works in the fields of analysis, analytic number theory, and combinatorics.

**Tammo tom Dieck** is a German mathematician, specializing in algebraic topology.

**Vladimir Georgievich Turaev** is a Russian mathematician, specializing in topology.

- ↑ Personal web page at Vanderbilt University
- ↑ Personal web page at Berkeley
- ↑ Personal web page at Auckland
- ↑ "Fellows". Royal Society. Retrieved 5 November 2010.
- ↑ "The Queen's Birthday and Golden Jubilee Honours 2002" (5 June 2002) 57
*New Zealand Gazette*1553. - ↑ Special Honours List (12 August 2009) 118
*New Zealand Gazette*2691 - ↑ List of Fellows of the American Mathematical Society, retrieved 26 January 2013.
- ↑ 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. - ↑ 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.

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)

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