Mathematical Sciences: Research in Pseudo-Riemannian Geometry

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Gregory Galloway will continue his studies of Lorentzian geometry. This is an area which overlaps both physics and mathematics. The study of events from a relativistic point of view leads to different invariants which in turn result in the study of different notions of distance, called Lorentzian metrics. The geometric phenomena to be studied are related to singularities in relativistic space time. Galloway will try to obtain further results building on his recent progress on the splitting theorem. The physical motivation for this work is the study of rigidity phenomena in the arena of singularity theory of general relativity. He will also study problems related to the existence of closed geodesics in pseudo- Riemannian manifolds. These are known to exist in compact Riemannian manifolds. Galloway will try to use a dynamic approach to the case where the metric is indefinite.