Vaughan F. Jones

Vanderbilt University


Election Year: 1999
Primary Section: 11, Mathematics
Membership Type: Member

Research Interests

My research is on all aspects of the theory of von Neumann algebras-closed self-adjoint algebras of operators on Hilbert space. Von Neumann algebras are part of the mathematical framework of quantum physics. They are a noncommutative generalization of probability theory and are an infinite dimensional extension of semisimple algebra. The basic examples can all be obtained from ergodic theory and dynamical systems. Statistical mechanics leads immediately to von Neumann algebra questions. A particular product of the recent interaction with low-dimensional topology was the appearance of a polynomial invariant of knotted curves in three-dimensional space. This led to topological quantum field theory, which interacts directly with subfactors, but the polynomial continues to be mysterious and I am interested in it for its own sake.

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