Mathematical Sciences: Hodge Structures and L2 Cohomology

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9505040 Stern The proposed research has to do with the Hodge theory of singular or noncompact varieties. The investigator proposes to realize the intersection cohomology of a projective variety as an explicit complex of differential forms equipped with a Hodge filtration. He also proposes to construct harmonic automorphic representatives of de Rham cohomology classes of locally symmetric spaces. Varieties are a central object in geometry and algebra as they arise as solutions to polynomial equations in various dimensions. Intersection cohomology is a way to understand how these varieties are situated in space by looking at their various intersection properties.