Mathematical Sciences: Diophantine Geometry and Differential Algebraic Geometry

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9500331 Buium Professor Buium will work in arithmetic geometry specifically problems in Diophantine geometry. He will use techniques from differential algebraic geometry to study Lang's conjecture, the semi-abelian case of Mazur's conjecture as well as relationships between the abc conjecture and logarithmic Kodaira dimension. 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. Professor Buium's research even includes a component coming from classical analysis. 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.