Mass for the large and for the small

Seeking a meaningful geometric (physical) invariant to describe a spacetime has sparkled researches in both mathematics and physics. In this talk, we will first see the fundamental progress made by Schoen-Yau and Witten on ADM (Arnowitt-Deser-Misner) mass. Then, we will see the progress on quasilocal masses in recent years. In particular, we would discuss the Hamiltonian formulation and the behaviour of quasilocal masses with the presence of apparent horizons.