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

西蒙9504456 提出了两个相关的研究课题：能量极小化映射的奇异性和曲率流。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，为此他最近获得了Bocher奖。除了继续这项研究-这可能会导致一个决议的重要猜想断言，极小的能量分层流形-几个问题的曲率流提出。 提出的曲率流问题模型广泛的现象，如肥皂膜，不混溶流体和晶体生长的动力学，并在该地区的非线性抛物型偏微分方程。

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.