Professor Rohrlich will work on several problems connected with the realization of Galois representations of Mordell-Weil groups of elliptic curves. In particular, whether certain irreducible Artin representations occur and if so what are their multiplicities. 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.
