Mathematical Sciences: Galois Covers of Curves

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Harbater This award supports the work of David Harbater on Galois covers of algebraic curves. Prof. Harbater's work involves number theory and geometry. He intends to use his recently established result, Abhyankar's conjecture, to use patching techniques to construct Galois Covers of curves. This is research primarily in the field of algebraic geometry. This field has had a revolutionary flowering in the past quarter century as techniques from number theory and algebra have found geometric application. Algebraic geometry is the study of curves that can be defined in the plane by the simplest equations, namely polynomials. Galois covers of curves are particular examples that have strong symmetries. The techniques of algebraic geometry now find application in such diverse fields as physics, theoretical computer science, and robotics. ***