|AMMCS-2013 Venue: Wilfrid Laurier
University Campus in Waterloo, Canada
AMMCS-2013 Plenary Talk
Computer involvement in the classification of small index subfactors
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.