Polyhedral computation, discrete optimization and quantum information

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The purpose of this grant was to provide funds for the new Geometric Computation Laboratory at Kyoto University which I have now established. This laboratory is concerned primarily with the following three research topics : polyhedral computation, discrete optimization and quantum information. The common theme linking these three topics is high dimensional geometry, and in particular, the study of polyhedra and related convex bodies. In addition to high quality theoretical results, the Geometric Computation Laboratory has been developing software that allows the results to be used widely in the engineering and scientific community.