Mathematical Sciences: Dynamical Systems, Geometry and Quasiconformal Homeomorphisms

首席研究员将继续他的研究 几何学和动力系统其中一个主要部分的 研究将扩展费根鲍姆普适性的验证 猜想到所有的真实的指数奇点。他还将 继续发展Chern-Weil理论 共形结构第三个项目涉及层压 理论的黎曼曲面，这可能会导致一个普遍的 Teichmuller理论以希尔伯特空间为模型。 该奖项将支持一般领域的研究， 微分几何和全局分析。微分几何 是研究空间的几何形状 和空间上定义的分析概念。全球分析是 对物体的整体几何和拓扑性质的研究 一个空间，通过拼凑当地的信息。的应用 这些数学领域的其他科学包括 复杂的分子结构，液-气边界， 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.