Mathematical Sciences: Ergodic Theory and Topological Dynamics

首席研究员将在三个方面进行研究 动力系统的相关领域。第一个领域涉及 具有两个或多个间断的最小间隔交换， 问它是否是素数。第二个研究领域涉及 Teichmuller测地线流和第三个领域涉及 具有固定锥的平坦黎曼曲面的模空间 奇点 该奖项将支持一般领域的研究， 动力系统一个非常简单和容易的过程， 局部理解会变得非常复杂，非线性， 很难在全球范围内进行分析。动力系统是研究 从本地到全球的关系。许多物理系统可以 最好是用这一领域的数学建模，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 investigator will conduct research in three related areas of dynamical systems. The first area concerns the minimal interval exchange with two or more discontinuities and asks whether it is prime. The second area of research involves the Teichmuller geodesic flow and the third area concerns the moduli space of flat Riemannian surfaces with fixed cone singularities. 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.