Mathematical Physics and Algebraic Geometry Seminar

Speaker: Thomas Creutzig (University of Alberta)

Title: Verlinde’s formula in logarithmic conformal field theory

Abstract: Two-dimensional conformal field theories lead to rich mathematical structure. For example its chiral algebra is a vertex algebra and the axioms of rational conformal field theory define modular tensor categories. A highlight of this development was Verlinde’s formula of rational conformal field theory, a formula that computes tensor product rules from modular data of characters.

Nowadays one is interested in logarithmic conformal field theories, in particular the underlying representation categories of the vertex algebras are not semi-simple and usually also not finte. Modular data and Verlinde’s formula become quite a mystery and I will explain how to resolve it.