Professor Schoen will work on the relation between Chow groups and Hodge theory. He will study the torsion subgroup as well as the Bloch-Beilinson conjectures. 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.
