Modular Tensor Categories, Quantum Groups and Vertex Algebras - Lecture 1

Dive into the first lecture of a four-part series exploring the interconnections between modular tensor categories, quantum groups, and vertex algebras. Focus on modular tensor categories with an emphasis on nonsemisimple theory. Gain insights into these advanced mathematical concepts as part of the Workshop on Quantum symmetries: Tensor Categories, Topological quantum field theories, and Vertex algebras. Explore the foundations of these complex topics from the perspective of the lecturer, setting the stage for deeper discussions on quantum groups, Nichols algebras, conformal quantum field theory, and the logarithmic Kazhdan–Lusztig conjecture in subsequent lectures.