## July 5: Introduction to planar algebras

### Emily Peters

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.