�@The Positive Mass Conjecture in 3 dimensions states that the 
mass of an asymptotically flat 3-manifold is positive when the manifold 
has nonnegative scalar curvature. This was first proved by Schoen and Yau 
using minimal surfaces techniques. Witten's proof is based on the analysis 
of the Dirac operator. Unlike a 3-manifold, a higher dimensional manifold 
need not be spin. In this talk, I will present joint work with Mark Stern 
towards proving the Positive Mass Conjecture in higher dimension.