Professor Greenberg will work on several problems connected with a generalized Iwasawa theory. He intends to study the Selmer group in certain infinite extensions of the rational numbers and in certain families of p-adic representations. 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.
