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Delve into the fascinating world of fusion rings in this comprehensive lecture presented by Joost Slingerland at the Dublin Institute for Advanced Studies. Explore these simple yet powerful mathematical structures that describe generalized addition of charges and generalize finite groups. Learn about their applications in physics and mathematics, and discover the challenges in creating a comprehensive list of small examples. Investigate the potential for more intricate and useful structures compatible with fusion rings, such as tensor categories and modular tensor categories, and their associations with particle models in 1+1D or 2+1D featuring topological interactions. Starting from the basics, gain insights into methods for discovering fusion rings, including computer-assisted approaches, and explore techniques for identifying corresponding category structures. Examine intriguing examples, including rings with non-Abelian fusion, and discuss practical applications to particle braiding on wire networks in this 2-hour and 25-minute deep dive into the subject.
