Dr. Simon Wood
Lie theory beyond category O in conformal field theory and vertex
Affine Lie algebras provide the means for constructing some of the best
understood conformal field theories or vertex operator algebras. If the
level of the affine Lie algebra is non-negative integral, then the
integrable modules form a modular tensor category (among many other
properties, this implies an action of the modular group on characters).
In this talk I will give an overview of why this is highly desirable
from the perspective of conformal field theory and some new results on
modular properties and their consequences at certain non-integral
levels, called admissible levels. No prior knowledge of vertex operator
algebras or conformal field theory will be assumed. I will do my best to
motivate everything through Lie theory.