Geometric realization of vertex algebras on the moduli space of stable curves

Motivated by the study of sheaves of conformal blocks attached to affine Lie algebras, I will present in this talk an analogous geometric realization attached to vertex algebras. In particular, we will see how, thanks to the Virasoro uniformization theorem, it is possible to associate to certain representations of conformal vertex algebras, projectively flat sheaves on the moduli space of stable curves. Our construction extends the sheaves to nodal curves, and allows to explicitly compute the Atiyah algebra acting on these sheaves as in the prior case as well.This is joint work with Angela Gibney and Nicola Tarasca.