John Beem will continue his research in Lorentzian geometry. This is an area of differential geometry which provides the mathematical foundations of relativity. It involves the study of indefinite or Lorentzian metrics in place of the more usual Riemannian metrics. Beem will study conditions which imply the stability of geodesic incompleteness. This has already been studied in the context of certain big bang models. He will also investigate the influence of pseudoconvexity on geodesic systems. Pseudoconvexity arises in the global solvability of pseudodifferential equations and is useful in geometry as an internal form of completeness.
