Mathematical Sciences: Galois Structures, Capacity Theory and Intersection Theory

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Professor Chinburg will work on Galois Module Structure for Schemes and the connection between capacity theory and intersection theory on varieties. In particular he will work on Euler characteristics using equivariant Riemann-Roch theorems. He will also work on limits of metrizied cycles in arbitrary codimension. 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.