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.
