Braided Fusion Categories - Lecture 3

Explore the third lecture in a series on braided fusion categories, delivered by Dmitri Nikshych at the Centre de recherches mathématiques (CRM) Workshop on Quantum symmetries. Delve into the algebraic theory of semisimple braided tensor categories, also known as fusion categories, and their applications in quantum symmetries. Learn about centralizers, or categorical "orthogonal complements," and the concept of non-degeneracy in braided fusion categories. This 53-minute talk is part of a comprehensive course designed to be accessible to graduate students, covering topics such as representation theory of quantum groups, topological quantum field theories, Galois theory for Jones-von Neumann subfactors, and topological phases of matter. Gain insights into the structure and classification of these important mathematical objects that play a crucial role in describing various non-commutative symmetries.