Vaughan Jones

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.