set for the Einstein equations. This operator reflects the geometry of the underlying

manifold in a manner similar to the Dirac operator appearing in Witten's proof of the

Positive Mass Theorem. By analyzing linear-growth null spacetime harmonic functions

and their level sets, we obtain a rather approachable refinement of the Positive Mass Theorem

for asymptotically flat 3-dimensional initial data sets. Applications to asymptotically hyperbolic

initial data sets are also considered. The work I will discuss includes various collaborations with

Hugh Bray, Sven Hirsch, Marcus Khuri, Daniel Stern, and Yiyue Zhang.