Professor Crew will study overconvergent isocrystals on algebraic varities of characteristic p. He hopes to characterize those isocrystals with finite dimensional cohomology or at least obtain a reasonable criterion for finite-dimensionality for them. 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.
