Professor Prasad will work on arithmetic, geometric and group theoretic questions related to semi-simple groups over local and global fields. He intends to work on the congruence subgroup problem for anisotropic semi-simple groups over global function fields. He also intends to study principal bundles over certain smooth 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.
