Demetre Kazaras, Duke University

Title: The spacetime Laplace equation on initial data sets for Einstein's equations

Abstract: This talk will consider a 'null spacetime Laplace' operator on an initial data
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.