Professor Vojta will work in arithmetic geometry specifically finiteness statements for rational and integral points on varieties. In particular he wants to continue to explore insights into the analogies between diophantine approximations and Nevanlinna theory. 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.
