Mathematical Sciences: Hodge Theory, L 2-Cohomology and Intersection Homology

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9423689 Zucker Professor Zucker will study locally symmetric spaces via methods of algebraic geometry. In particular he wants to study the relationship between various Hodge structures and cohomology of a locally symmetric variety. He will also study extensions of intersection cohomology to a class of real analytic varieties with a view to proving a version of the decomposition theorem. This is research in the field of algebraic geometry. Algebraic geometry is 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. ***