Introduction to Vertex Algebras

Harvard FAS

Vertex algebras provide a rigorous mathematical framework for two-dimensional conformal field theory. This course offers a comprehensive introduction to the subject, bridging its algebraic and geometric aspects. The first half focuses on local constructions, covering the foundational axioms and key examples of vertex algebras (such as Kac-Moody and Virasoro algebras). The second half transitions to the global framework, introducing conformal blocks associated with a vertex algebra and vertex…