Mathematical Sciences: Geometry of Teichmuller Space

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The principal investigator will study the geometry and manifold structure of Teichmuller space. He will focus his investigations on the infinite as well as finite dimensional cases. The project will have applications to three-dimensional topology, string theory, dynamical systems, and iteration of rational functions. A Teichmuller space consists of the set of all "markings" of a surface with a finite number of holes and a finite number of punctures. For example, a punctured inner tube has one hole and one puncture. A marking is a distinguished basis for the fundamental group of the surface. This might consist of several circles about the holes and punctures. The principal investigator will apply his theories of Teichmuller space to a variety of other applications within mathematics.