Mathematical Sciences: Analytic Geometry and Arithmetic Groups

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This award supports the research in deformation theory and arithmetic groups of Professor John Millson of the University of Maryland at College Park. Dr. Millson has proposed to work in two main areas: first, he will apply the methods of rational homotopy theory to deformation problems in algebraic geometry; and second, he will continue his research on the cohomology of discrete subgroups of orthogonal and unitary groups. This is research in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.