Mathematical Sciences: Arithmetic of Motives and Shimura Varieties

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Professor Blasius will continue his work on Shimura varieties and their associated motives. He will study motives attached to Hilbert modular forms using the stable trace formula and endoscopy. He will also study reductions mod p of these varieties. 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.