Appears in collection : Not Only Scalar Curvature Seminar

This is a survey of some of my joint works with my students and postdocs on geometry of scalar curvature that have been done in recent years. In the first part of the talk, I will discuss Gromov’s fill-in problem, which has a deep connection with quasi-local masses in General Relativity. In the second part of the talk, I will discuss Llarull type theorems on complete manifolds with positive scalar curvature.