An Introduction to Fusion Rings - Part I

Dive into a comprehensive lecture on fusion rings, their applications in physics and mathematics, and their connection to particle models. Explore the fundamental concepts of fusion rings as simple mathematical structures describing generalized charge addition. Discover how fusion rings generalize finite groups and the challenges in creating a comprehensive list of small examples. Investigate the potential for more intricate structures compatible with fusion rings, such as tensor categories and modular tensor categories, and their implications for particle models in various dimensions. Learn about methods for finding fusion rings, including computer-assisted approaches, and techniques for identifying corresponding category structures. Examine interesting examples, including rings with non-Abelian fusion, and discuss applications to particle braiding on wire networks. This 1 hour and 48 minute lecture, presented by Joost Slingerland at the Dublin Institute for Advanced Studies, assumes no prior knowledge and provides a thorough introduction to the fascinating world of fusion rings.