Mathematical Sciences: Kodaira Dimensions of Fiber Products and the Distribution of Rational Points

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Caporaso 9505140 Professor Caporaso will work on two problems in algebraic geometry. She intends to study the Kodaira dimension of fiber products of certain families of curves whose general member is of general type. She will also study the geometry of the universal Picard variety. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter- century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and roboticq. ***