Professor Ulmer will work on the arithmetic of elliptic curves and automorphic forms over function fields. In particular, he intends to work on analogues of the conjecture of Mazur that asserts that the group of rational points on an elliptic curve defined over a function field over a finite field in a certain Zp extension is finitely generated. 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.
