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Fellows Directory

Vaughan Jones

Vaughan Jones

Professor Vaughan Jones FRS


Elected: 1990


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.

Interest and expertise

Subject groups

  • Mathematics
    • Pure mathematics
  • Astronomy and physics
    • Mathematical and theoretical physics


analysis, Algebra, Topology, von Neumann algebras, Knot theory, Mathematical physics


  • Fields Medal

    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.

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