Mathematical Sciences: Ergodic Theory and Dynamics over Teichmuller Space

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9503542 Veech The proposed research lies in the area of complex dynamical systems. The proposer wants to evaluate certain integrals over the Teichmuller moduli space coming from an identification of the Teichmuller space with the space of cone metrics. Techniques for the study of the billiard in a regular polygon are expected to play an important role. The Teichmuller moduli space corresponds to a family of pretzel-like surfaces known as compact Riemann surfaces (of a fixed genus); these surfaces play an important role in studying complex-valued functions. The proposed research aims to give a geometric description of some of these surfaces.