Vaughan Jones’s first work was a complete classification of the action of finite groups on von Neumann algebras of type II. He went on to define an ‘index’ for a subfactor of a II1 factor, and found its possible values, most strikingly the unsuspected discrete series 4 cos2(pi/n). This work has profoundly changed the perspective of its whole field. It also produced a completely new family of representations of the braid groups, and Vaughan showed how these gave a new polynomial invariant for knots. On one side this transformed knot theory, while in another direction it opened up a new field embracing statistical mechanics, conformal quantum field theory, and the quantisation of Lie groups. Vaughan’s most recent work concerns planar algebra and representations of Richard Thompson’s groups F and T.
Sir Vaughan Jones KNZM FRS died on 6 September 2020.
Analysis, Algebra, Topology, von Neumann algebras, Knot theory, Mathematical physics
For his discovery of an unexpected link between the mathematical study of knots – a field that dates back to the 19th century – and statistical mechanics, a form of mathematics used to study complex systems with large numbers of components.