AG Mathematische Physik, Dietmar Bisch (Vanderbilt): New subfactors with small Jones index

Dietmar Bisch (Vanderbilt)

New subfactors with small Jones index

Abstract: Since Vaughan Jones introduced the theory of subfactors in

1983, it has been an open problem to determine the set of Jones indices of

irreducible, hyperfinite subfactors. Not much is known about this set.

My student Julio Caceres and I have recently shown that certain intersting

indices between 4 and 5 are realized by new hyperfinite subfactors with
Temperley-Lieb-Jones standard invariant. This leads to a conjecture
regarding Jones‘ problem. Our construction involves commuting squares,
a graph planar algebra embedding theorem, and a few tricks that allow us
to avoid solving large systems of linear equations to compute invariants
of our subfactors. I will give some background to make the talk accessible
to non-experts.