Title: Quantum graphs and spin models

Abstract: Spin models for singly-generated Yang-Baxter planar algebras are known to be  determined by certain highly-regular classical graphs such as the Higman-Sims graph. Examples of spin models include the Jones and Kauffman polynomials. We will explore the notion of higher-regularity for quantum graphs as well as their potential to encode spin models. Time allowing, we will give examples of non-classical graphs with these properties and aspects of the associated (quantum) spin models.