Mathematical Sciences: Deformations, Hodge Theory, and LP Cohomology

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Professor Zucker will work on locally symmetric spaces as well as transcendental methods in algebraic geometry. He will also study Torelli type questions for fibre spaces. Professor Karpishpan will work on Hodge theory from the point of view of deformation theory, using differential Lie algebras. This project falls into the general area of arithmetic geometry -a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.