Mathematical Sciences: Ergodic Theory and Topological Dynamics

首席研究员将在动力系统的三个相关领域进行研究。第一个领域涉及两个或多个不连续的最小区间交换，并询问它是否为素数。第二个研究领域涉及Teichmuller测地流，第三个领域涉及具有固定锥奇点的平坦黎曼曲面的模空间。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 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.