The HADES seminar on Tuesday, **December 7th**, will be given by **Shi-Zhuo Looi** at **5 pm** on Zoom.

**Speaker**: Shi-Zhuo Looi

**Abstract**: We discuss the proof of sharp pointwise decay for linear wave equations, and then scattering and sharp pointwise decay for power-type nonlinear wave equations. These results hold on a general class of asymptotically flat spacetimes, which are allowed to be either nonstationary or stationary. The main ideas for the linear problem include local energy decay and commuting vector fields, while the nonlinear problem uses r-weighted local energy decay and Strichartz estimates. For either problem, the initial data are allowed to be large and non-compactly supported.