Professor Keating will work on the Igusa tower that arise in the theory of modular curves, the action of the automorphism group of certain formal groups defined on the moduli space of deformations and finally to characterize the fields arising from formal groups obtained by deformations. 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.
