Mathematical Sciences: Dynamical Systems, Geometry and Quasiconformal Homeomorphisms

首席研究员将继续他在几何和动力系统方面的研究。本研究的一个主要部分是将Feigenbaum普适性猜想的验证扩展到所有实指数奇点。他还将继续为可测量的共形结构发展陈-韦尔理论。第三个项目涉及黎曼曲面的层压理论，这可能导致以希尔伯特空间为模型的通用Teichmuller理论。该奖项将支持微分几何和全局分析领域的研究。微分几何是研究空间几何与空间上定义的解析概念之间关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑特性。这些数学领域在其他科学中的应用包括复杂分子的结构、液气边界和宇宙的大尺度结构。

The principal investigator will continue his research in geometry and dynamical systems. One of the main parts of the research will extend verification of the Feigenbaum universality conjecture to all real exponent singularities. He will also continue to develop the Chern-Weil theory for measurable conformal structures. A third project involves a lamination theory for Riemann surfaces which may lead to a universal Teichmuller theory modeled on Hilbert space. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.