For those who aren't familiar with the Virasoro or Temperley-Lieb algebras, I include some definitions: • The (universal envelopping algebra of the) Virasoro algebra is the * …

I'm hoping to learn something about planar algebras while attacking a planar algebra question with an undergrad research student. I'm thinking about reading this paper, as Kuperber …

I work in planar algebras and subfactors, where the idea of path algebras on a graph (alternately known as graph algebras, graph planar algebras, etc.) is quite useful. The partic …

In the same vein as Kate and Scott's questions, why are fusion categories interesting? I know that given a "suitably nice" fusion category (which probably means adding adjectives s …

As I understand it, there is a subfactor whose principal graph is the affine Dynkin diagram $\tilde{A}_n$. Since every vertex has two neighbors, does that mean the space of 1-boxes …

In Jones's paper "Planar Algebras I", Theorem 4.2.1 establishes that an extremal finite index subfactor admits a spherical C*-planar algebra structure, and Theorem 4.3.1 establishe …

This is related to Noah's recent question about solving quadratics in a number field, but about an even earlier and easier step. Suppose I have a huge system of linear equations, …

Are there any good short expositions of planar algebras out there? I am interested primarily in seeing the main definition and some explicit examples.

Reidermeister's theorem states that the set of knots, modulo ambient isotopy, is isomorphic to the planar algebra generated by crossings, modulo Reidemeister moves. This planar alg …