Thomas Creutzig, University of Alberta
Title: Modularity in Logarithmic conformal field theory
Abstract: Rational conformal field theory and vertex operator algebras have two structures describing important parts of it. On the one hand this is the representation category and on the other one torus one-point functions, that is a vector valued modular form. Both carry actions of the modular group and they are intimitly connected via Verlinde's formula. I will outline what happens if one first drops the condition on complete reducibility of modules (the CFT is logarithmic then) and then secondly in addition allowing for infinitely many simple objects. In both cases modular properties of characters cover structure of the representation ring, thus suggesting an exciting connection between modern modular objects like mock modular forms and false theta functions and logarithmic modular tensor categories.
