Mathematical Sciences: Capacity Theory, Green's Functions, and Intersection Theory

数学科学：容量理论、格林函数和交集理论

• 批准号: 9500842
• 负责人: Robert Rumely
• 金额: $ 4.42万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500842&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Capacity; Theory; Green

This awards supports the research of Professor P. Aluffi to work in algebraic geometry. He will work on problems deriving from the study of hypersurface singularities. He hopes to find a new formula for MacPherson's Chern class and to extend result son duality of projective varieties. He hopes to apply some of these results to the study of combinatorial questions on graphs. 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P. Aluffi教授在代数几何方面的研究。他将研究从超曲面奇点的研究中衍生出来的问题。他希望为MacPherson的陈氏类找到一个新的公式，并推广射影变量对偶性的结果。他希望将这些结果中的一些应用到图的组合问题的研究中。这项研究是在代数几何领域进行的，代数几何是现代数学中最古老的部分之一，但在过去的10年里，它已经发展到解决了几个世纪以来一直存在的问题的程度。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。