Mathematical Sciences: Center for Computation & Visualization of Geometric Structures

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This proposal from the University of Minnesota, requests funds to establish a Science and Technology Center for Computation and Visualization of Geometric Structures. The Director of the Center will be Professor Albert Marden. The Center involves collaboration among eighteen mathematicians from thirteen institutions throughout the U.S. and Europe. In addition to faculty from the University of Minnesota, the Center will involve participants from Brigham Young, Cornell, Courant Institute, Harvard, Princeton, Rutgers, SUNY Stony Brook, University of California, San Diego, as well as Ecole Normale Superieur, Paris, the University of Warwick, and AT&T Bell Laboratories. Under the aegis of the Geometry Supercomputer Project at Minnesota, these researchers have been collaborating for the past three years. Through this collaboration they have demonstrated their ability to make such a distributed Center function. The subject of mathematics, an extremely rich and varied territory, has had a tendency to fragment into many subdisciplines, with little communication between them, or their closely related fields, such as computer science. The goal of the Center is to tie these differently perceived fields together under the unifying topic of geometry and geometric representation on the computer. The Center's scientific program is based on a core of scientific investigations whose origins are in "pure" mathematics as well as models of physical phenomenon. It is organized into five groups: topology; geometry and symmetry dynamics; geometric optimization; computation, geometry and graphics; and fractal geometry. The proposed research includes a range of high-level mathematics centered on geometry utilizing high-level computer science centered on geometry, in the environment of a high-quality laboratory for computation, graphics, and visualization. Through the common thread of visualization, the research forms a coherent body. The Center will provide leadership in typing diverse fields of mathematics and computer science together and will facilitate knowledge transfer between fields. In addition, the solutions of some of the proposed problems will require the development of software tools that could reach beyond the basic mathematical areas involved and have important applications to research in other scientific fields, such as molecular biology, where visualization modeling are essential. This Center will stimulate enhanced activity in precollege education and in the development of human resource.//