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Description

I will present an upcoming work with J. Luk (Stanford), where we develop a general method for understanding the late time tail for solutions to wave equations on asymptotically flat spacetimes, which is applicable to nonlinear problems on dynamical backgrounds. In addition to its inherent interest, such information is crucial for studying problems involving the interaction of waves with a spatially localized object; indeed, our motivation for developing this method comes from the Strong Cosmic Censorship Conjecture. I will explain how our method recovers and refines Price's law for linear problems on stationary backgrounds, and also how it shows that the late time tails are in general different(!)  from the linear stationary case in the presence of nonlinearity and/or a dynamical background.