Mathematical Sciences: Hodge Theory and Algebraic Geometry

数学科学：霍奇理论和代数几何

• 批准号: 9102046
• 负责人: Mark Green
• 金额: $ 17.1万
• 依托单位: University of California-Los Angeles
• 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: 1991-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102046&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hodge; Theory; Algebraic

This awards supports the research of Professor M. Green to work in algebraic geometry. He will work on Hodge theory, the geometry of projective varieties, and algebraic curves. The techniques used will be a mixture of algebraic and differential- geometric. 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M教授的研究。绿色至 研究代数几何。 他将致力于霍奇理论， 射影簇几何和代数曲线。 的 使用的技术将是代数和微分的混合物- 几何的 这项研究是在代数几何领域，其中之一， 现代数学中最古老的部分，但其中一个蓬勃发展， 在过去的10年里，它解决了一些问题， 屹立了几个世纪 最初，它处理的是 平面由最简单的方程，即多项式。 今天 field不仅使用代数方法，还使用分析方法 和拓扑学，相反，它被广泛用于那些 领域的 此外，它已经证明自己在各种领域都很有用， as physics物理，theoretical理论computer计算机science科学，cryptography密码学，coding编码 理论与机器人