Apparaît dans la collection : Higher Structures in Holomorphic and Topological Field Theory

In the late 1990s, Borcherds gave an alternate definition of some vertex algebras as "singular commutative rings" in a category of functors depending on some input data (A,H,S). He proved that for a certain choice of A, H, and S, the singular commutative rings he defines are indeed examples of vertex algebras. In this talk I will explain how we can vary this input data to produce categories of chiral algebras and factorization algebras (in the sense of Beilinson-Drinfeld) over certain complex curves X. We’ll discuss the failure of these constructions to give equivalences of categories and obstructions to extending this approach to more general varieties X.