We all learned with immense sorrow that Vaughan Jones died on Sunday September 6th.

I met him in the late seventies when he was officially a student of André Haefliger but contacted me as a thesis advisor which I became at a non-official level. I had done in my work on factors the classification of periodic automorphisms of the hyperfinite factor and Vaughan Jones undertook the task of classifying the subfactors of finite index of the hyperfinite factor among which the fixed points of the periodic automorphisms give interesting examples.By generalizing an iterative construction which I had introduced he was first able to show that the indices of subfactors form the union of a discrete set with a continuum exactly as in conformal field theory. But his genius discovery was when he understood the link between his theory of subfactors and knot theory which is the geometry of knots in three space!

This is really a fantastic discovery that led to a new invariant of knots : the Jones polynomials!

This discovery was afterwards dressed using functional integrals but the real breakthrough is indisputably due to Vaughan Jones.

To me his discovery is one of the great jewels of the unity of mathematics where a seemingly remote problem such as the classification of subfactors of finite index turned out to be deeply related to a fundamental geometric problem!

For this reason I do not hesitate to affirm that Vaughan Jones' discovery is one of pure genius and that his work has all characteristic features that grant it immortality.

## No comments:

Post a Comment