Explore the intricacies of braided fusion categories in this comprehensive lecture by Dmitri Nikshych. Delve into the algebraic theory of semisimple braided tensor categories, their structure, and classification. Learn about basic properties and examples, centralizers and non-degeneracy, (de)-equivariantizations, and the core of braided fusion categories. Discover the process of gauging braided fusion categories and their Picard groups. Examine Witt equivalence of non-degenerate categories and the categorical Witt group. Suitable for graduate students, this 53-minute talk covers topics such as braided groups, centers, restrictions, fusion category bridges, centralizers, sub-categories, non-degenerate categories, symmetrical categories, braided equivalence, and evaluation. Part of the Workshop on Quantum symmetries: Tensor Categories, Topological quantum field theories, and Vertex algebras, this lecture provides insights into the representation theory of quantum groups and their applications in various fields, including topological quantum field theories, Galois theory for Jones-von Neumann subfactors, and topological phases of matter. Read more