AMMCS-2013 Plenary Talk

Computer involvement in the classification of small index subfactors

Vaughan Jones

Abstract: A subfactor of index k is a generalisation of a permutation group on a set of size k. Except that the number k is no longer required to be an integer- it is a real number. While the listing of all transitive permutation groups on a set of size 5 would be covered in a first class in group theory, the subfactor result has only recently been completed thanks to Morrison, Peters, Snyder and many other authors. And their computers. The classification begins with the enumeration of all possible "Principal graphs", which in index less than or equal to 4 are the usual singly laced Coxeter graphs. Ten more subfactors exist with index between 4 and 5, some of which are only accessible via computer computations. I will present these results and the local blend of computer calculation and theory, and the extent to which the computer calculations may or may not be necessary.

Sir Vaughan F. R. Jones (KNZM FRS FRSNZ) is a New Zealand mathematician, known for his work on von Neumann algebras and Knot Theory. He was awarded a Fields Medal in 1990 at the ICM in Kyoto. Jones is currently a distinguished professor of mathematics at Vanderbilt University. He previously served as a professor at the University of California, Berkeley and a Distinguished Alumni Professor at the University of Auckland.