Mathematical Sciences: Shimura Varieties and Abelian Varieties

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Professor Silverberg will continue her work on Shimura varieties. In particular, she plans to study adelic representations attached to points on canonical models of arithmetic quotients of bounded symmetric domains. She also intends to work on questions about the fields obtained by adjoining torsion points on Abelian Varieties. 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.