Mathematical Sciences: Algebraic Geometry and Gauge Theory

数学科学：代数几何和规范论

• 批准号: 9203940
• 负责人: Robert Friedman
• 金额: $ 10.73万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203940&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Geometry; Gauge

This awards supports the research of Professor R. Friedman to work in algebraic geometry. He will continue to study the connections between the algebraic and smooth properties of 4-manifolds. In particular, he will try to decide if every complex surface diffeomorphic to a rational surface is itself rational and whether one can characterize smoothly embedded 2-spheres of certain types lying on a complex surface. 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R.弗里德曼教授在代数几何领域的研究。他将继续研究4-流形的代数性质和光滑性质之间的联系。特别是，他将试图确定是否每个与有理曲面微分同胚的复杂曲面本身都是有理的，以及是否可以光滑地刻画位于复杂曲面上的某些类型的嵌入的2-球面。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，它发展到了解决了几个世纪以来的问题的地步。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，这个领域不仅使用代数的方法，而且还使用分析和拓扑学的方法，相反，它在这些领域被广泛使用。此外，它在物理、理论计算机科学、密码学、编码理论和机器人学等领域都证明了自己的有用。