Vaughan Jones | Academic Influence

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Vaughan Jones

Mathematics

#164

World Rank

#392

Historical Rank

Topology

#12

World Rank

#23

Historical Rank

Measure Theory

#1153

World Rank

#1473

Historical Rank

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Mathematics

Vaughan Jones's Degrees

PhD Mathematics University of Geneva
Bachelors Mathematics University of Auckland

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Why Is Vaughan Jones Influential?

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According to Wikipedia, Sir Vaughan Frederick Randal Jones was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990. Early life Jones was born in Gisborne, New Zealand, on 31 December 1952. He was brought up in Cambridge, New Zealand, where he attended St Peter's School. He subsequently transferred to Auckland Grammar School after winning the Gillies Scholarship, and graduated in 1969 from Auckland Grammar. He went on to complete his undergraduate studies at the University of Auckland, obtaining 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, and won him the Vacheron Constantin Prize.

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Vaughan Jones's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Index for subfactors (1983) (1607)
A polynomial invariant for knots via von Neumann algebras (1985) (1563)
Hecke algebra representations of braid groups and link polynomials (1987) (1497)
On knot invariants related to some statistical mechanical models (1989) (344)
A Polynomial Quantum Algorithm for Approximating the Jones Polynomial (2005) (277)
Property T for von Neumann Algebras (1985) (217)
Invariants of torus knots derived from quantum groups (1993) (173)
Algebras associated to intermediate subfactors (1997) (166)
Von Neumann Algebras (2020) (144)
Planar algebras (1999) (142)
Actions of finite groups on the hyperfinite type ₁ factor (1980) (137)
The Annular Structure of Subfactors (2001) (126)
On a certain value of the Kauffman polynomial (1989) (118)
The classification of subfactors of index at most 5 (2013) (107)
Subfactors and Knots (1991) (106)
Introduction to subfactors (1997) (100)
The Planar Algebra of a bipartite graph (2000) (99)
Some unitary representations of Thompson's groups F and T (2014) (88)
ASYMPTOTICALLY INVARIANT SEQUENCES AND APPROXIMATE FINITENESS (1987) (81)
Singly generated planar algebras of small dimension (2000) (68)
Quadratic Tangles in Planar Algebras (2010) (66)
Graph Invariants Related to Statistical Mechanical Models: Examples and Problems (1993) (65)
In and around the origin of quantum groups (2003) (65)
Actions of compact abelian groups on semifinite injective factors (1984) (62)
Metaplectic link invariants (1989) (59)
A No-Go Theorem for the Continuum Limit of a Periodic Quantum Spin Chain (2016) (58)
A ${\text{II}}_1 $ factor with two nonconjugate Cartan subalgebras (1982) (51)
The embedding theorem for finite depth subfactor planar algebras (2010) (50)
Hilbert space representations of the annular temperley-lieb algebra (2006) (47)
AN ORTHOGONAL APPROACH TO THE SUBFACTOR OF A PLANAR ALGEBRA (2008) (46)
Period two automorphisms of UHF C*-algebras (1982) (41)
Random matrices, free probability, planar algebras and subfactors (2007) (40)
Lissajous knots and billiard knots (1998) (39)
Intermediate subfactors with no extra structure (2004) (34)
Loop Models, Random Matrices and Planar Algebras (2010) (33)
Subfactors of Index Less Than 5, Part 3: Quadruple Points (2011) (33)
The Jones Polynomial (2006) (33)
A semi-finite algebra associated to a subfactor planar algebra (2011) (28)
Scale invariant transfer matrices and Hamiltionians (2017) (28)
Some Properties of Masa’s in Factors (1982) (25)
A semi-finite algebra associated to a planar algebra (2009) (24)
Singly generated planar algebras of small dimension, Part II (2003) (24)
Models of finite group actions. (1983) (24)
On the Haagerup and Kazhdan properties of R. Thompson’s groups (2018) (23)
On a family of almost commuting endomorphisms (1994) (23)
Singly generated planar algebras of small dimension, Part III (2014) (23)
On the Construction of Knots and Links from Thompson’s Groups (2016) (20)
NOTES ON SUBFACTORS AND STATISTICAL MECHANICS (1990) (20)
Knot theory and statistical mechanics (1990) (20)
TWO SUBFACTORS AND THE ALGEBRAIC DECOMPOSITION OF BIMODULES OVER II1 FACTORS (2008) (19)
Pythagorean representations of Thompson's groups (2018) (19)
A $\mathrm{II}_1$ factor anti-isomorphic to itself but without involutory antiautomorphisms. (1980) (18)
The Homflypt polynomial and the oriented Thompson group (2016) (18)
Intersections of finite families of finite index subfactors. (2004) (16)
Central sequences in crossed products of full factors (1982) (15)
On the symmetric enveloping algebra of planar algebra subfactors (2011) (14)
On spectral measures for certain unitary representations of R. Thompson's group F (2019) (14)
An invariant for group actions (1979) (14)
Von Neumann algebras in methematics and physics (1990) (13)
The Algebraic Approach (1991) (12)
Irreducibility of the Wysiwyg Representations of Thompson’s Groups (2019) (12)
COMMUTING TRANSFER MATRICES AND LINK POLYNOMIALS (1992) (11)
Bergman space zero sets, modular forms, von Neumann algebras and ordered groups (2020) (8)
Hilbert modules over a planar algebra and the Haagerup property (2015) (7)
Operator Algebras and Applications: Subfactors and related topics (1989) (6)
On the origin and development of subfactors and quantum topology (2009) (5)
Von Neumann algebras in mathematics and physics : plenary address, International Congress of Mathematicians, Kyoto, Japan, August 1990 (1990) (5)
Quantum mechanics over fields of non-zero characteristic (1976) (4)
A Note on Free Composition of Subfactors (2021) (4)
Relative cohomology of groups (1984) (4)
Actions of finite groups on the hyperfinite type II[subscript 1] factor (1980) (3)
Infinite Index Subfactors and the GICAR Categories (2014) (3)
Von Neumann Algebras and Ergodic Theory of Group Actions (2008) (3)
New Inside Out. Upper Intermediate (2010) (2)
Knots, groups, subfactors and physics (2015) (2)
Editorial (dedication of this issue to Huzihiro Araki) (1993) (2)
Loop Models, Random Matrices and Planar Algebras (2012) (2)
Matrices over the natural numbers: Values of the norms, classification, and variations (1989) (1)
Towers of multi-matrix algebras (1989) (1)
O A ] 2 5 M ay 2 02 1 Irreducible inclusions of simple C ∗-algebras (2021) (1)
Subfactors and Applications (2020) (1)
Book Review: Quantum symmetries on operator algebras (2001) (1)
Knots in mathematics and physics (1992) (1)
Uffe Haagerup–In Memoriam (2016) (1)
Highly transitive imprimitivities (2006) (1)
From Subfactors to Quantum Topology In memory of Vaughan Jones (2022) (1)
Motzkin algebras and the An tensor categories of bimodules (2020) (1)
Introduction to Subfactors: Commuting squares (1997) (0)
Title On the symmetric enveloping algebra of planar algebra subfactors Permalink (2011) (0)
Infinite Index Subfactors and the GICAR Categories (2015) (0)
The principal and dual graphs (1997) (0)
The Knot Polynomial _ (1991) (0)
Knots, groups, subfactors and physics (2016) (0)
Finite von Neumann Algebras with Finite Dimensional Centers (1989) (0)
Subfactors of Index Less Than 5, Part 3: Quadruple Points (2012) (0)
A HIERARCHY OF COMPUTABLY ENUMERABLE DEGREES, II: SOME RECENT DEVELOPMENTS AND NEW DIRECTIONS (2021) (0)
Planar algebras : between dimensions two, three and infinity (2000) (0)
Commuting sqares, subfactors, and the derived tower (1989) (0)
Random matrices , amalgamated free productsand subfactors of the von Neumann algebra ofa (0)
Introduction to Subfactors: Subfactors and index (1997) (0)
Group Actions and Subfactors (1991) (0)
Some basic facts (1997) (0)
S[p]in models, subfactors and link invariants (1993) (0)
2011 Kemeny Undergraduate Lecture (2011) (0)
Vertex and spin models (1997) (0)
In 1984 Jones discovered an astonishing relationship between a construction in Von Neumann Algebras and a theorem in geomet- (2007) (0)
Some Moment calculations (2008) (0)
Isomorphisms of Automorphism Groups of Type II Factors (1981) (0)
Values of the Index, Virasoro Algebra (1991) (0)
KNOTS, BRAIDS AND STATISTICAL MECHANICS (1990) (0)
Knots and Links (1991) (0)
A No-Go Theorem for the Continuum Limit of a Periodic Quantum Spin Chain (2017) (0)
Askey, Rokhlin Elected to NAS (1998) (0)
Singly generated planar algebras (2014) (0)
Knots and Statistical Mechanics (1991) (0)
How Quantum Theory and Statistical Mechanics Gave a Polynomial of Knots (2014) (0)
Construction of Examples, Further Structure (1991) (0)
The Braid Group and Its Representations (1991) (0)
Classifying subfactors and fusion categories (2015) (0)
The annular stru ture of subfa tors (2000) (0)
MEDNYKH ’ S FORMULA VIA LATTICE TOPOLOGICAL QUANTUM FIELD THEORIES (2017) (0)
Quantum spin chains , correspondences and subfactors (2012) (0)
Title Random matrices , free probability , planar algebras and subfactors Permalink (0)

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