Department of Mathematics

Vaughan Jones has accepted a faculty position as Distinguished Professor with the Department of Mathematics beginning in the fall of 2011. A preeminent mathematician who comes to Vanderbilt from the University of California, Berkeley, Jones will be a tremendous addition to the department’s already strong research group in operator algebras.

Jones’ contributions to mathematics have their origins in his work on subfactors, inclusions of certain highly noncommutative algebras of operators on Hilbert space known as von Neumann algebras. Von Neumann algebras were introduced by the legendary John von Neumann in the 1920s in his investigations of quantum physics, ergodic theory, and group representation theory. They were the central objects of Alain Connes’ work in the ’70s that led to his Fields Medal in 1982, the first one in operator algebras.

Jones introduced in the early ’80s a notion of index for a von Neumann subalgebra (or a subfactor) and found that indices of subfactors take on only very special values. He discovered that this totally unexpected rigid behavior was related to the existence of a new braid group representation that comes with each subfactor. Jones used his representation to construct a new polynomial invariant for knots and links, now called the Jones polynomial. This amazing discovery led to a whole new branch of modern mathematics, perhaps most adequately called?quantum topology. Jones? work paved the way to many new and exciting interactions between a priori widely separate areas of mathematics and physics, including statistical mechanics, conformal field theory, knot theory, low dimensional topology, von Neumann algebra theory, quantum groups, representation theory, category theory, and quantum computing. His most recent work on subfactors, planar algebras, and random matrix theory has uncovered many new and beautiful structures and connections and has generated a lot of interest and excitement among researchers in the above-mentioned areas.

In 1990, Jones received the Fields Medal for his work. The Fields Medal is awarded once every four years to mathematicians not over 40 years of age for outstanding discoveries in mathematics. It is widely viewed as the Nobel Prize of mathematics.

Jones has received many honors for his work in addition to the Fields Medal. He was elected a Fellow of the Royal Society in 1990 and has also been elected to the United States National Academy of Sciences (1999), the American Academy of Arts and Science (1993), and the Norwegian Royal Society of Letters and Sciences (2001). He received the Onsager Medal (2000), the Prix Mondial Nessim Habif (2007) and is a Knight Companion of the New Zealand Order of Merit (2009). He holds many honorary doctorate degrees from universities all over the world.

Jones will be a member of the Department of Mathematics? Center for Noncommutative Geometry and Operator Algebras, directed by Professor and Department Chair Dietmar Bisch. This group includes about 20 faculty members, students and postdoctoral researchers whose research interests are in von Neumann algebras, subfactors and planar algebras, operator algebraic K-theory, coarse geometry, index theory, and several other related fields. The center organizes the annual Noncommutative Geometry and Operator Algebras Spring Institute, directed by Professor Alain Connes.

“We are thrilled that Vaughan will join the mathematics department,” says Chair Dietmar Bisch, who has collaborated with Jones for more than 15 years. “His presence will enhance our research profile enormously and give students and postdocs a chance to learn from one of the foremost mathematicians.”

Professor Jones is scheduled to teach a course on subfactors and planar algebras in fall 2011.

(For a profile of Jones that appeared in the Vanderbilt View, see “Fields Medalist Brings Informal Style to Vanderbilt.”)