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Explore new approaches to fundamental results in mathematical general relativity through this 37-minute conference talk delivered by Lorenzo Mazzieri at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into PDE-based methods for proving the positive mass theorem and the Riemannian Penrose inequality. Examine the interplay between various concepts of mass and quasi-local mass found in both classical and recent literature. Gain insights from this presentation, which was part of the Workshop on "Non-regular Spacetime Geometry" held at ESI in March 2023.
