Existence of good moduli spaces and applications

Recently Alper, Hall and Rydh gave general criteria when a moduli problem can locally be described as a quotient. We report on a joint project with Jarod Alper and Daniel Halpern-Leistner in which we use these results to show general existence and completeness results for good coarse moduli spaces. In the talk we will focus on aspects that illustrate how the geometry of moduli problems formulated in terms of algebraic stacks gives a new point of view on classical methods for the  construction of moduli spaces - and provides a method that applies in situations where classical approaches seem unavailable. This allows to apply the method to interesting classes of moduli problems.