Professor Grant will work on various aspects of the arithmetic of curves of genus two. He will study integer points on these curves, certain units arising from curves of genus two, and new methods for calculating the Mordell-Weil rank of such curves. 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.
