Abstract: If Riemannian manifolds are used to model suitable time slices in a physical spacetime, natural
curvature assumptions are often given in terms of their scalar curvature. For noncompact manifolds,
fundamental results on scalar curvature include the Riemannian positive mass theorem and the Riemannian
Penrose inequality. For compact manifolds with nonempty boundary, finding the right notion of quasi-local
mass is one of the most significant problems in relativity. In this talk, we aim to give an introduction to some of the known results involving scalar curvature and also to discuss some related open questions.
