The seminar will meet in Jingzhai (静斋) 105, Tsinghua University. In this seminar, we will study wave equations particularly nonlinear wave equations, from a geometric perspective, and inspired by the dynamics in general relativity. Among the topics ofinterest are black holes, stability, long-term dynamics,low-regularity, fluids, and shocks. We will have a combination of external and local speakers, including students.