17th Seminar on Conformal Field Theory

Thomas Creutzig: Representation Theory for logarithmic CFTs

Representation categories of  vertex algebras associated to rational CFTs are modular tensor categories and Verlinde’s formula holds. Representation categories of vertex algebras associated to logarithmic CFTs are not semisimple and usually not finite. I will discuss and illustrate  the underlying structure that guarantees that these categories are ribbon and that Verlinde’s formula holds.

Jens Eberhardt: Sheaves on Stratified Spaces

In this talk, we study constructible sheaves on spaces stratified via a Gm-action.
We show how to understand the gluing data of these categories geometrically using hyperbolic localisation and the Drinfeld-Gaitsgory interpolation space.
In particular, we apply this framework to flag varieties. Here, we explain how the gluing data can be understood explicitly in terms of a new multiplicative structure on open Richardson varieties.

Lastly, we discuss applications in symplectic geometry and geometric representation theory.
This is joint work with Catharina Stroppel.

Michael Tuite: Zhu recursion for VOAs on general genus Riemann surfaces

We describe Zhu recursion for a vertex operator algebra (VOA) and its modules on a genus g Riemann surface in the Schottky uniformization. We describe how $n$-point correlation functions have a natural residue expansion in terms (n − 1)-point functions with universal coefficients given by holomorphic forms and derivatives of the Bers quasiform. We describe genus g Ward identities in terms of novel differential operators which act on meromorphic forms. We discuss Heisenberg VOA examples where the Ward identities lead to novel differential equations for the partition function and various classical structures such as the bidifferential of the second kind, holomorphic 1-forms, the prime form and the period matrix. This talk is based on joint work with Michael Welby.