Mathematical Sciences: Properties of the Igusa Local Zeta Function

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This career advancement award supports the research of Professor Meuser to study the Igusa local zeta function. In particular she plans to explore connections between the explicit form of the local zeta function and the geometry of the associated variety. 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.