Mathematical Sciences: Research Proposal on Arithmetic Geometry

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Chai 95-02186 Professor Chai will continue his work on moduli spaces of Abelian varieties. In particular, he wishes to study the density of Hecke orbits in certain Shimura varieties. He also wishes to study the canonical lifting of Abelian varieties and certain classes of motives. He hopes to apply his results to prove the existence of certain canonical integral models. 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.