Mathematical Sciences: Galois Structure on Schemes & Capacity Theory on Varieties

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Professor Chinburg will work on a theory for a Galois Module Structure for Schemes and the connection between capacity theory and intersection theory on varieties. In particular, he will work on generalizing arithmetic intersection theory to limits of arithmetic cycles. 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.