The ADM mass of an isolated gravitational system is a geometric invariant measuring the total mass due to matter and other fields. I’ll describe how to compute this invariant (in 3 spatial dimensions) by studying harmonic functions as well as solutions to other elliptic equations. Recent results in this context will be presented, focusing on applications to the asymptotically flat and asymptotically hyperbolic versions of the Positive Mass Theorem. Comparisons to minimal surfaces and Dirac-harmonic spinors will be made. I’ll also consider the question: How flat is an asymptotically flat manifold with very little total mass?

Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact Peter McGrath host to get the link.