Mathematical Sciences: Deformations of Complex Structures

主要研究人员将在复平面的经典情况下研究动力系统。一名研究员将研究谐波测度与分析能力之间的关系。另外两位研究者将继续研究与Kleinian群和Teichmuller理论相关的模空间。研究跨越了一个复杂变量的经典分析、群论和微分几何。该奖项将支持动力系统一般领域的研究。一个非常简单的、局部容易理解的过程，可能变得极其复杂、非线性，难以全局分析。动力系统就是对这种局部到全局关系的研究。许多物理系统都可以用这个数学领域来最好地建模，包括流体流动和湍流、复杂的生物系统、机械系统和化学反应。

The principal investigators will study dynamical systems in the classical case of the complex plane. One investigator will study the relationship between harmonic measure and analytic capacity. The other two investigators will continue their research on the moduli spaces associated with Kleinian groups and Teichmuller theory. The research spans classical analysis in one complex variable, group theory, and differential geometry. This award will support research in the general area of dynamical systems. A process which is very simple and easy to understand locally can become extremely complicated, nonlinear, and difficult to analyze globally. Dynamical systems is the study of this local to global relationship. Many physical systems can best be modeled using this area of mathematics including fluid flow and turbulence, complex biological systems, mechanical systems, and chemical reactions.