This grant supports the research of W. McCallum and D. Ulmer to work in arithmetic geometry. Professor McCallum will study descent on Fermat's curve. Professor Ulmer will study the p-adic valuations of coefficients of modular forms as well as the Iwasawa theory for elliptic 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.
