The two pillars of rational conformal field theory and rational vertex operator algebras are
modularity of characters, and the interpretation of its category of modules as a modular …

A two-dimensional chiral conformal field theory can be viewed mathematically as the
representation theory of its chiral algebra, a vertex operator algebra. Vertex operator …

In this paper, we present a theory of tensor products of classes of modules for a vertex
operator algebra. We focus on motivating and explaining new structures and results in this …

We review the construction of braided tensor categories and modular tensor categories from
representations of vertex operator algebras, which correspond to chiral algebras in physics …

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We describe the construction of the genus-zero parts of conformal field theories in the sense
of G. Segal from representations of vertex operator algebras satisfying certain conditions …

Rational chiral conformal field theories are organized according to their genus, which
consists of a modular tensor category $\mathcal {C} $ and a central charge c. A long-term …

In contrast with the finite dimensional case, one of the distinguished features in the theory of
infinite dimensional Lie algebras is the modular invariance of the characters of certain …

In conformal field theory, intertwining operators (or chiral vertex operators) are very
important and useful tools. For rational conformal field theories many important concepts …

We discuss our recent results on the representation theory of W-algebras relevant to
Logarithmic Conformal Field Theory. First we explain some general constructions of W …