We will discuss the defocusing energy-critical nonlinear wave equation. For deterministic and smooth initial data, it is widely known that the solutions scatter, i.e., they asymptotically behave like solutions to the linear wave equation. In this talk, we will show that this scattering behavior persists under random and rough perturbations of the initial data. As part of the argument, we will discuss techniques from restriction theory, such as wave packet decompositions and Bourgain’s bush argument. Speaker(s): Bjoern Bringmann (UCLA)