Mathematical Sciences: Topics in Arithmetic Geometry and K-theory

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Professor Gillet will continue his work on Arakelov theory and arithmetic Riemann-Roch type theorems. He will also work on Gersten's conjecture in Algebraic K-theory and connections between Lichtenbaum's conjectures on K-theory and Regulators and arithmetic intersection theory. 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.