Mathematical Sciences: Tidal Accelerations Along Null Geodesics and Causal Boundaries of Product Spacetimes

约翰·比姆将继续他的洛伦兹几何研究。这是微分几何的一个领域，它为相对论提供了数学基础。它涉及到对不确定或洛伦兹度量的研究，而不是更常见的黎曼度量。Beem将研究暗示测地线不完备稳定性的条件。这已经在某些大爆炸模型中得到了研究。他还将研究伪凸性对测地线系统的影响。伪凸性产生于伪微分方程的整体可解性中，在几何中作为完备性的一种内在形式是有用的。

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.