Mathematical Sciences: Invariants of Singular Germs and Polynomials

数学科学：奇异胚和多项式的不变量

• 批准号: 9203482
• 负责人: Andras Nemethi
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203482&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Invariants; Singular; Germs

This awards supports the research of Professor A. Nemethi to work in algebraic geometry. He will work on invariants of singularities and global polynomials. He plans to study the behavior of the signature for composed singularities. He hopes to see the connections between the signature of surface singularities and the Casson invariant of links. 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A. Nemethi教授在代数几何方面的研究。他将研究奇异点的不变量和全局多项式。他计划研究组合奇点的签名行为。他希望看到表面奇点的特征和环的卡森不变量之间的联系。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。