The definition of the Turaev-Viro TQFT (which Chris will talk about next week) requires some sort of graphical calculus -- a method for doing algebraic calculations using topological doodles. Planar algebras are the graphical calculus I understand best, so that's what I'm going to talk about. I will mostly talk about the example of the Temperley-Lieb planar algebra, and the structure needed to define a Turaev-Viro TQFT from Temperley-Lieb. Time permitting, I'll also talk about subfactors and their relation to planar algebras -- possibly setting us up for a future talk about operator-algebraic CFT? But note that I will not say anything about xFT this week.