Vertex Operator Algebras and Integrable Systems - Lecture 2

Explore the second lecture in a series on Vertex Operator Algebras and Integrable Systems delivered by Distinguished Visiting Professor Boris Feigin at Kyoto University. Delve into the construction methods of vertex operator algebras, focusing on the use of "screenings" to find vertex operator subalgebras within known ones and the extension technique for embedding algebras into larger structures. Examine W-algebras and their applications, along with the production of D-modules on geometric objects. Learn about Hitchin systems and D-modules in both usual and quantum geometric Langlands. Understand the implications of screening systems corresponding to affine root systems, which lead to structures related to non-conformal field theories and contain integrable systems with commutative algebras of KdV type. This 2-hour and 38-minute lecture was presented on July 23-26, 2018, at the Graduate School of Science Building No. 3, Room 127, as part of the Top Global Course Special Lectures series.