I will explain the notion of a singular ring and sketch how singular rings provide field and vertex algebras introduced by Borcherds and Kac. All of these notions make sense in general symmetric monoidal categories and behave nicely with respect to symmetric lax monoidal functors. I will provide a complete classification of singular rings if the tensor product is a cartesian product. This applies in particular to categories of topological spaces or (algebraic) stacks equipped with the usual cartesian product. Moduli spaces provide a rich source of examples of singular rings. By combining these ideas, we obtain vertex and field algebras for each reasonable moduli space and each choice of an orientable homology theory. This generalizes a recent construction of vertex algebras by Dominic Joyce.
