Mathematical Sciences: Problems in Complex Analysis

首席研究员将继续他的研究C-R 几何学和全纯映射他会用分析的方法 例如对d”-算子的估计以及几何 技术，包括由Monge-Ampere确定的folliations 操作符.在另一个方向，首席研究员将 研究多复变量多项式映射的迭代。 他将继续他的调查性质的朱莉娅集 以及映射的遍历性。 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 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.