Mathematical Sciences: Galois Covers of Curves

这个奖项支持David Harbater在代数曲线的Galois覆盖方面所做的工作。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猜想，使用补丁技术来构造曲线的Galois覆盖。这主要是在代数几何领域的研究。在过去的四分之一个世纪里，随着数论和代数的技术得到几何应用，这一领域取得了革命性的成就。代数几何是研究可以用最简单的方程，即多项式在平面上定义的曲线的学科。曲线的伽罗瓦覆盖是具有强对称性的特殊例子。现在，代数几何技术在物理、理论计算机科学和机器人等不同领域得到了应用。***

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. ***