Mathematical Sciences: Research in Circle Packings, Quasiconformal Geometry and Complex Function Theory

主要研究者将研究圆形填充， 拟共形映射要研究的一个主要问题是 Koeba单值化猜想指出， 扩展复平面共形同胚于 在扩展平面上的圆域。将使用的技术 这一研究与拟共形理论密切相关 地图 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 study circle packings and quasiconformal mappings. One main problem to be studied is the Koeba uniformization conjecture which states that any domain in the extended complex plane is conformally homeomorphic to a circle domain in the extended plane. The techniques to be used in this study are closely related to the theory of quasiconformal maps. 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.