Mathematical Sciences: Harmonic Mappings, Discrete Groups, and Hodge Theory

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This award supports the research in Algebraic Geometry of Professors James Carlson and Domingo Toledo of the University of Utah. Their work is in Hodge theory, and their aim is to attack the problem of classifying harmonic mappings from compact Kaehler manifolds to locally symmetric spaces of noncompact type, with particular attention to rigidity and factorization theorems. 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 theoretical Computer Science and in Robotics.