Algebraic and Arithmetic Geometry Seminar
# Geometry of vertex operator algebras on moduli of curves

→
Europe/Rome

Aula Riunioni (Department of Mathematics)
### Aula Riunioni

#### Department of Mathematics

Description

The physically-inspired theory of *conformal blocks *allows one to construct vector bundles on moduli spaces of curves with remarkable geometric and combinatorial properties. This theory uses as input the representations of some non-commutative algebras. A classical example is provided by the representations of *affine Lie algebras*, and the resulting vector bundles have been studied at great length in the last thirty years, yielding extraordinary insights on moduli spaces of curves. In this talk, I will present how some fundamental results of the classical theory of conformal blocks extend to the more general setting provided by replacing affine Lie algebras with *vertex operator algebras*. Specifically, I will discuss an extended factorization property and new cohomological field theories. This is joint work with Chiara Damiolini and Angela Gibney.