Mathematical Sciences: Problems in Arithmetic Geometry and Complexity Theory

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Professor Teitelbaum will work on the p-adic analytic theory of modular curves and its arithmetic implications. He will study higher weight invariants of modular forms, the arithmetic of Shimura varieties and the arithmetic of Drinfeld modular curves. 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.