Reimundo Heluani (Rio de Janeiro)
Abstract
In 1996 Y. Zhu showed that traces of modules of certain infinite dimensional Lie algebras, or more generally vertex algebras (under some finiteness conditions) satisfy natural modular differential equations. In particular they are convergent series. These traces give rise to vectors in the space of conformal blocks in genus one, or the (dual of) 0-th chiral homology in genus 1. In this talk I'll show how to associate to certain extensions of modules a trace functional that generalizes that work of Zhu. We show that these functionals converge under some finiteness conditions on the vertex algebra and satisfy an explicit modular differential equation. Their meromorphic limits give rise to vectors in the (dual of) degree 1 chiral homology group in genus 1.
This is joint work with J. van Ekeren