Mathematical Sciences: Regularity and Singularity in Geometric Variational and Flow Problems

西蒙9504456提出了两个相关的研究主题：能量奇点最小化映射和曲率流。西蒙开创了研究能量最小化映射的顶维奇异集的分析技术，他最近因此而获得了布歇尔奖。除了继续这项研究--这可能导致解决断言能量最小化是分层流形的重要猜想--之外，还提出了关于曲率流的几个问题。提出的曲率流动问题模拟了一系列的现象，如肥皂膜的动力学、不混溶流体和晶体生长，属于非线性抛物型偏微分方程组。

Simon 9504456 Two related topics of research are proposed: singularities of energy minimizing maps and curvature flows. Simon pioneered analytic techniques for studying the top-dimensional singular set of an energy minimizing map, for which he recently won the Bocher prize. In addition to continuing this research - which could lead to a resolution of the important conjecture asserting that minimizers of energy are stratified manifolds - several problems on curvature flows are proposed. Proposed curvature flow problems model a wide range of phenomena, such as the dynamics of soap films, immiscible fluids and crystal growth, and lie in the area of nonlinear parabolic partial differential equations.