Mathematical Sciences: Research in Riemann Surfaces and Dynamical Systems

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The principal investigator will use methods from Riemann surface theory to study problems in dynamical systems. In particular, he will use the theory of quadratic differentials and Teichmuller theory to study the ergodic theory of measured folliations, interval exchange transformations, and rational billiards. 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.