Planar algebras and their representations

Abstract: 

Planar algebra is an algebra of a certain class of pictures on the Euclidean plane. Vaughan Jones introduced these objects as an invariant of a special class of (inclusion of) von Neumann algebras called `subfactors'. Subsequently, planar algebras turned out to have deep connections with various fields, namely, quantum groups, category theory, graph theory, etc. In this talk, we will begin by recalling the definition of planar algebras and their representations. We will then go on to discuss an example coming from the action of finitely generated groups and compute their representations.