Title: Higher dimensional issues arising in gravitational theory
Speaker: Richard Schoen (University of California - Irvine)
Abstract: The Einstein equations were originally posed for a four dimensional spacetime, but they make sense in any higher dimension as well; in fact, their study is of interest both in the physics of string theory and the mathematical study of the scalar curvature. The methods described in the previous lecture do not generalize easily to all cases. In general dimensions the minimal hypersurface methods encounter problems with singularities in dimension 8 or more, and the Dirac operator methods require that the manifold be a spin manifold. We will describe how the singularities of minimal hypersurfaces can be dealt with to prove some of the results, including the general positive energy theorems in all cases.
