Mathematical Sciences: Representations of p-adic Groups

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Professor Reeder will continue his work on the representations of p-adic algebraic groups. He will seek explicit results about the representations containing an Iwahori-fixed vector. This work exploits the interplay between p-adic harmonic analysis and complex algebraic geometry. 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.