Categorifying Connections in Fusion Categories and Subfactors

Explore the intricate relationship between fusion categories and subfactors in von Neumann algebras through this 48-minute conference talk delivered by Emily Peters at the Canada-Mexico-US Conference on Representation Theory, Noncommutative Algebra, and Categorification. Delve into the translation of Ocneanu's paragroup theory into tensor categorical language, examining how connections on bipartite graphs correspond to functors from Temperley-Lieb-Jones categories into graph categories. Gain insights into the bidirectional influence between fusion categories and subfactors, understanding how subfactors provide unique examples of fusion categories and how fusion category techniques contribute to subfactor construction and classification. Uncover the mathematical foundations that bridge these complex concepts, enhancing your understanding of advanced algebraic structures and their applications in representation theory.