Vaughan Frederick Randal Jones

Vaughan Frederick Randal Jones, Sir Vaughan, passed away on September 6, 2020, in Nashville, Tennessee. Vaughan was born on December 31, 1952, in New Zealand where he grew up, studied at the University of Auckland and received his Master of Science degree in 1973.

After graduating from the University of Auckland, Vaughan went to study mathematics as a graduate student at the Université de Genève, Switzerland. In 1979 he completed his doctoral (Docteur ès Sciences ) thesis, "Actions of finite groups on the hyperfinite II₁ factor," with André Haefliger as his formal adviser. In 1980 he moved to the United States, where he first was a postdoc at UCLA and then a faculty member at the University of Pennsylvania. He joined the Department of Mathematics at U.C. Berkeley in 1985.

In 2011 he moved to Vanderbilt University, where he became the Stevenson Distinguished Professor of Mathematics. He was also a Distinguished Alumni Professor at the University of Auckland and a founding Director and Chairman of the New Zealand Mathematics Research Institute during 1994-2020. He helped develop New Zealand’s mathematical expertise by organizing annual summer workshops at various venues in New Zealand for over 25 years. Attendees included local mathematicians and graduate students as well as invited mathematicians from all over the world.

Vaughan is famous for his contributions to the theory of von Neumann algebras, for the Jones invariant of knots, and for results in related areas of statistical mechanics. His construction of this invariant of knots was presented in the paper "A polynomial invariant for knots via von Neumann algebras" published in 1985 in the Bulletin of the American Mathematical Society. Perhaps his most remarkable result on the theory of von Neuman algebras is presented in his 1983 paper "Index for subfactors" published in Inventiones Mathematicae. His contributions had enormous impact on many areas of mathematics and mathematical physics.

For his work on knot polynomials and von Neumann algebras, Vaughn received the most prestigious prize in mathematics, the Fields Medal, in 1990. His contributions to mathematics were recognized in many other awards and honors. Among the most distinguished are his election as a Fellow of the Royal Society (U.K., 1990), to the American Academy of Arts and Science (1993) and to the U.S. National Academy of Sciences (1999). He was awarded the Rutherford Medal by the Royal Society of New Zealand (1991) and was appointed Distinguished Companion of the New Zealand Order of Merit (DCNZM) for services to mathematics (2002), which was upgraded to a Knight Companion (2009). He received the Onsager medal of Trondheim University, Norway (2000), the Prix Mondial Nessim Habif, Geneva, Switzerland (2007), as well as a number of honorary doctorates. In 2019, he was awarded the ICCM International Cooperation Award for his strong support of the Chinese mathematical community throughout his career.

Vaughan inspired several generations of mathematicians. More than 30 graduate students obtained their Ph.D.s under his supervision. Several of them became well-known mathematicians. He created a strong sense of community among his students, holding weekly “beer and pizza” dinners on Fridays after his subfactor seminar and organizing math retreats that included windsurfing, kitesurfing and skiing. He was a generous man and an inspiring teacher. At Berkeley he taught at all levels, from low-division calculus classes to topics graduate classes and earned one of the top department ratings for his teaching.

Vaughan also served on many advisory boards including the Fields Institute of Mathematics (Toronto, Canada), the Erwin Schrodinger Institute (Vienna, Austria), the Mathematical Sciences Research Institute (Berkeley, California), and the Fudan University Science and Innovation Award Committee (Shanghai, China). He was elected vice-president of the American Mathematical Society in 2004 as well as a vice-president of the International Mathematical Union, 2015-2018.

Vaughan is survived by his wife, Martha “Wendy” Jones, Associate Professor of Medicine, Heath and Society at Vanderbilt University, and by their three children and two grandchildren.

Nicolai Reshetikhin
2021

See also: Dietmar Bisch, David E. Evans, Robion Kirby, and Sorin Popa, Memorial Tribute "Memories of Vaughan Jones,'' Notices of the American Mathematical Society, October 2021.