Mathematical Sciences: Polylogarithms, Mixed Motives, and Special Values of L-Functions

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Goncharov 9400010 Professor Goncharov will work on the relationship between both classical and modern theories of the polylogarithm and special values of L-functions of varieties. He will also explore connections between algebraic k-theory and motivic Galois groups. The goal is an explicit computation of the Beilinson regulator for arithmetic 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.