Explore a 45-minute conference talk on nonlocal generalizations of Green hyperbolicity presented by Christopher Fewster at the Workshop on "Non-regular Spacetime Geometry" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the concept of Green-hyperbolic operators on globally hyperbolic spacetimes and their importance in studying quantum field theory on curved spacetimes. Discover how the speaker extends Green hyperbolicity to accommodate nonlocal perturbations, with applications in modeling noncommutative spacetimes and aspects of quantum field measurement theory. Learn about the conditions for the existence of Green operators and the potential obstacles, such as smooth solutions to homogeneous equations with past or future-compact support. Gain insights into this advanced topic in mathematical physics and its implications for our understanding of spacetime geometry and quantum field theory.