Mathematical Sciences: Geometry and Topology of Surfaces

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Robert Penner is studying geometric topological problems with implications for particle physics. There is a highly developed, essentially combinatorial, theory of conformal classes of punctured Riemann surfaces. Some recent work at once suggests new approaches to old problems in the Teichmuller theory and in the theory of the mapping class group. Furthermore, there is a great deal of interplay between these new results and several central problems in the string theory of high energy physics. This second interface should probably be regarded as one of co- development rather than one of application.