Professor Rumely will work on sectional capacity for adelic sets on projective varieties of arbitrary dimensions. He will develop properties of sectional capacity and attempt to prove the homogeneous form conjecture that on a variety of dimension d, the sectional capacity is determined by a homogeneous form of degree d+1. 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.
