Mathematical Sciences: Topics in Real Algebraic Geometry

数学科学：实代数几何专题

• 批准号: 9104427
• 负责人: Charles Delzell
• 金额: $ 4万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1994-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104427&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Real; Algebraic

This awards supports the research of Professors C. Delzell and J. Madden to work in real algebraic geometry. They will work on a general theory of local real algebraic geometry connecting singularities with intersections using notions from ordered fields. They also intend to work on relations between lattice ordered rings and real algebraic geometry, Lipschitz continuity and differentiability of abstract semialgebraic functions and smoothly varying solutions to Hilbert's 17'th problem. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover, it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.

该奖项支持C教授的研究。德尔泽尔 和J·马登研究真实的代数几何。 他们将工作 局部真实的代数几何的一般理论 奇点与交叉使用的概念从有序 领域的 他们还打算研究晶格之间的关系 序环与真实的代数几何，Lipschitz连续性 抽象半代数函数的可微性和 希尔伯特第17问题的平滑变化解 这项研究是在代数几何领域，其中一个 现代数学中最古老的部分，但其中一个 在过去的10年里， 已经屹立了几个世纪 最初，它把数字 在平面上由最简单的方程定义，即 多项式 今天，该领域使用的方法不仅来自 代数，但也从分析和拓扑学，反过来说，它 广泛应用于这些领域。 此外，它还证明， 它本身在物理学、理论、 计算机科学、密码学、编码理论和机器人技术。