Mathematical Sciences: Deformations of Complex Structures

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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.