Mathematical Sciences: Intersection Theory and P-adic Dynamical Systems

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Keating 9500982 Professor Keating will work on problems in arithmetic geometry. He will try to compute the arithmetical intersection numbers for certain divisors on moduli spaces of abelian varieties. He also will study the general theory of p-adic dynamical systems from he point of view of the field of norms. Finally he wishes to study the actions of certain automorphism groups of formal groups on the moduli space of deformations of that group. 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.