Mathematical Sciences: Problems in Complex Analysis

首席研究员将继续他对C-R几何和全纯映射的研究。他将使用分析中的方法，如对d“算子的估计，以及几何技术，包括由Monge-Ampere算子确定的对开式。在另一个方向，主要研究人员将研究多项式映射在多个复变量中的迭代。他将继续研究Julia集的性质和映射的遍历性质。该奖项将支持在微分几何和全球分析的一般领域的研究。微分几何是研究空间几何和定义在该空间上的解析概念之间的关系的学科。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性质的学科。这些领域的数学在其他科学中的应用包括复杂分子结构、液体-气体边界和宇宙的大尺度结构。

The principal investigator will continue his study of C-R geometry and holomorphic maps. He will use methods from analysis such as estimates for the d"-operator as well as geometric techniques including folliations determined by the Monge-Ampere operator. In another direction, the principal investigator will study iterations of polynomial maps in several complex variables. He will continue his investigation of properties of Julia sets and the ergodic properties of the 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.