Extensions of Vertex Operator Algebras and Applications to Integrable Systems I

Explore advanced mathematical concepts in this distinguished lecture on vertex operator algebras and their extensions, delivered by Boris Feigin from Hebrew University of Jerusalem. Discover 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 tensor category techniques, and examine what possibilities emerge when working with deformed VOAs. Delve into practical applications, particularly focusing on 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 forms part of the CRM Distinguished Lectures in Mathematical Physics series and provides a comprehensive introduction to cutting-edge research in mathematical physics and algebra.