Mathematical Sciences: The Differential Geometry of PartialDifferential Equations

9505125布莱恩特拟议的研究位于外部差动系统领域。作者试图对具有非平凡守恒律的各类系统进行分类，并发展出计算给定系统可积扩张的有效算法。作者还希望了解控制系统的几何不变量，并研究控制算法。主要使用的工具是Cartan的等值方法和Cartan-Kahler理论。外微分系统推广了偏微分方程组；它们的研究是高度几何的，同时也是大量的计算。控制理论在制造业和机器人等领域得到了广泛的应用；所提出的研究可能有助于基于对所涉及的几何不变量的更深入的理解来创建更有效的设计算法。

9505125 Bryant The proposed research lies in the area of exterior differential systems. The proposer seeks to classify systems of various types which admit non-trivial conservation laws, and to develop effective algorithms for computing integrable extensions of a given system. The proposer also wishes to understand the geometric invariants of a control system and to investigate control algorithms. The main tools to be used are Cartan's method of equivalence and Cartan-Kahler theory. Exterior differential systems generalize systems of partial differential equations; their study is heavily geometric and heavily computational at the same time. Control theory is used extensively in such areas as manufacturing and robotics; the proposed research may help to create more efficient design algorithms based upon a deeper understanding of the geometric invariants involved.