The Representation Theory of Vertex Operator Algebras, Conformal Bootstrap and Segal's Axioms

Explore the representation theory of vertex operator algebras as a powerful framework for constructing and analyzing conformal field theories in this 57-minute mathematical lecture. Learn how basic algebraic data satisfying finiteness conditions can be used to construct spaces of states and correlation functions, while establishing fundamental assumptions of conformal bootstrap and Segal's axioms for conformal field theories. Review key results on conformal bootstrap and Segal's axioms derived through vertex operator algebra representation theory, and examine the potential implications of Liouville conformal field theory construction for cases where finiteness conditions are not satisfied. Gain insights into one of the most successful mathematical approaches to conformal field theory, bridging algebraic structures with physical theories through rigorous mathematical foundations.