Factorizing the index

The Batalin-Vilkovisky procedure for quantization of field theories naturally produces factorization algebras. In this talk, I will discuss issues that arise in studying families of BV theories, focusing on a natural class of holomorphic BV theories that bears a natural relationship with the Grothendieck-Riemann-Roch theorem. This joint work with Brian Williams should provide a higher-dimensional generalization of aspects of the relationship between the Virasoro algebra and the moduli of curves.