Mathematical Sciences: Intersection Theory, Mirror Symmetry and Computer Algebra

数学科学：交集理论、镜像对称和计算机代数

• 批准号: 9311386
• 负责人: Sheldon Katz
• 金额: $ 9.66万
• 依托单位: Oklahoma State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9311386&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Intersection; Theory; Mirror

9311386 Katz This grant supports the research of Professor S. Katz to work in algebraic geometry. He will work on the mirror symmetry conjecture that arose from superstring theory. He will also continue to develop a computer algebra package for doing intersection computations. 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. ***

小行星9311386 这项拨款支持S教授的研究。卡茨的工作在代数几何。他将致力于从超弦理论中提出的镜像对称猜想。他还将继续开发一个计算机代数包做交叉计算。 这项研究是在代数几何领域，这是现代数学最古老的部分之一，但在过去的10年里，它已经发展到解决了几个世纪以来的问题。最初，它处理由最简单的方程，即多项式在平面上定义的图形。今天，该领域使用的方法不仅来自代数，而且来自分析和拓扑学，相反，它被广泛用于这些领域。 此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人学等不同领域都很有用。 ***