**Title**: Planar algebras and proof by pictures

**Speaker**: Emily Peters (Loyola University of Chicago)

**Abstract**: Planar algebras are a formalization of “proof by pictures” techniques that are used in the study of knots, subfactors, and tensor categories, among other places. When one tries to directly construct a planar algebra, by generators and relations, one quickly runs into the standard problems, like: how do I decide if what I have is just a dressed-up version of the trivial planar algebra? Sometimes, one can answer this type of question by giving an "evaluation algorithm" based on the relations available. In this talk, I will define planar algebras and give some of my favorite examples of planar algebras with cool evaluation algorithms. No background beyond linear algebra will be assumed. If time permits, I will touch on recent results on the extended Haagerup planar algebras, which is joint work with Grossman, Morrison, Penneys and Snyder.

Colloquium URL: https://web.math.osu.edu/colloquium/