Root stack valuative criterion and applications

Recently, Bresciani and Vistoli proved a root stack valuative criterion for tame moduli spaces which has had applications to the arithmetic of stacks and to the geometry of moduli spaces of fibrations. In this talk I will discuss a generalization of this result to stacks with a good moduli space along with several applications. I will also discuss how to use the root stack valuative criterion to give a moduli theoretic perspective on the study of rational points on stacks. This is based on joint work with Inchiostro and Satriano, and with Park and Satriano respectively.