Mathematical Sciences: Galois Covers of Curves

这个奖项支持David在代数曲线的伽罗瓦覆盖上的工作。哈伯特教授的工作涉及数论和几何。他打算利用他最近建立的结果，Abhyankar的猜想，使用修补技术来构造曲线的伽罗瓦覆盖。这主要是代数几何领域的研究。在过去的25年里，随着数论和代数技术在几何上的应用，这一领域出现了革命性的发展。代数几何研究的是可以在平面上用最简单的方程，即多项式来定义的曲线。曲线的伽罗瓦覆盖是具有强对称性的特殊例子。代数几何技术现在在物理学、理论计算机科学和机器人技术等不同领域都有应用。＊＊＊

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. ***