Mathematical Sciences: Galois Covers of Curves

数学科学：曲线的伽罗瓦覆盖

• 批准号: 9400836
• 负责人: David Harbater
• 金额: $ 37.54万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400836&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Galois; Covers; Curves

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. ***

哈巴特尔 这个奖项支持工作的大卫Harbater伽罗瓦涵盖代数曲线。 Harbater教授的工作涉及数论和几何。 他打算使用他最近建立的结果，Abhyankar猜想，使用修补技术来构建曲线的伽罗瓦覆盖。 这主要是在代数几何领域的研究。 这个领域有一个 在过去的四分之一世纪里，随着数论和代数的技术在几何学中的应用，几何学出现了革命性的发展。代数几何是研究可以在平面上由最简单的方程，即多项式定义的曲线。 曲线的伽罗瓦覆盖是具有强对称性的特殊例子。 代数几何的技术现在发现在物理学、理论计算机科学和机器人学等不同领域的应用。 ***