This Presidential Young Investigator will work on Mordell- Weil lattices of elliptic surfaces, the size and structure of the Tate-Safarevic group and the connection to coding theory via the Barnes-Wall lattices. 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.
