On the Behavior of Solutions of Einstein's Equations and the Behavior of Ricci Flows

爱因斯坦的场方程，除了在天体物理学和宇宙学尺度上为当前最好的引力物理行为描述提供了基础之外，还提供了大量有趣的数学问题的来源。Isenberg教授将研究其中的几个问题，包括：爱因斯坦约束方程的解具有比目前已知的更一般的特征。爱因斯坦方程解中奇点的出现（即所谓的“强宇宙审查”猜想）数学流形和它们的几何形状之间的关系。（《利玛窦之流》）这项工作将增加数学和理论物理中思想和工具的相互作用。

Einstein's field equations, besides providing the basis for the best current description of the behavior of gravitational physics on the astrophysical and cosmological scale, also is the source of a rich collection of mathematically interesting questions. Prof. Isenberg will investigate several of these, including: 1. solutions of the Einstein constraint equations of a more general character than currently known 2. occurrence of singularities in solutions to Einstein's equations (i.e. the so-called "Strong Cosmic Censorship" conjecture) 3. the relationship between mathematical manifolds and their geometries (i.e. "Ricci flows") This work will increase the interaction of ideas and tools in mathematics and theoretical physics.