Mathematical Sciences: Presidential Young Investigator Award

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The principal investigator will continue his studies of intersection cohomology while partially supported by this Presidential Young Investigator award. In particular, he will work towards a proof of the Borel conjecture which would extend his solution with L. Saper of the Zucker conjecture. In two other projects, he will study singular algebraic varieties and a geometric interpretation of the zeta functions arising in his index theorem. Cohomology is the dual of homology. In cohomology theory spaces of functions on topological spaces are studied, while in homology theory the spaces themselves are graded by their algebraic connectivity properties. The principal investigator will work toward solving a deep conjecture concerning square- integrable cohomology as related to intersection cohomology.