Extensions of Vertex Operator Algebras and Applications to Integrable Systems II

Explore advanced mathematical concepts in this distinguished lecture from the Centre de recherches mathématiques focusing on vertex operator algebras and their extensions. Delve into the intricate relationship between vertex operator algebras (VOAs) and quantum groups, understanding how quantum groups function as symmetry groups of VOAs. Learn about the construction of extensions of classical VOAs using sophisticated tensor category techniques, and discover the possibilities that emerge when working with deformed VOAs. Examine practical applications of these theoretical frameworks, particularly in the context of algebras with a "large center" that serve as natural analogs of affine Kac–Moody algebras at the critical level. Gain insights into the connections between these mathematical structures and integrable systems, as well as their relevance to the geometric Langlands program. This presentation represents cutting-edge research in mathematical physics, offering a deep dive into the deformation theory of vertex operator algebras and their far-reaching implications for modern mathematical research.