Mathematical Sciences: Research in Algebraic Geometry

数学科学：代数几何研究

• 批准号: 9400918
• 负责人: Steven Kleiman
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400918&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Algebraic; Geometry

Kleiman This supports the research of Professors S. Kleiman and M. Artin with Dr. J. Pommersheim as a post-doctoral associate. Kleiman will continue to work on Buchsbaum-Rim multiplicity and equi-singularity. Artin will continue to work on the foundations of non-commutative algebraic geometry. Pommersheim will work on the connection between toric varieties and number theory. This is research in the field of algebraic geometry broadly conceived. Algebraic geometry itself is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics. ***

Kleiman 这支持 S. Kleiman 教授和 M. Artin 教授以及 J. Pommersheim 博士作为博士后助理的研究。 克莱曼将继续致力于 Buchsbaum-Rim 多重性和等奇异性的研究。 Artin 将继续致力于非交换代数几何的基础研究。波默斯海姆将致力于复曲面簇与数论之间的联系。 这是广义上的代数几何领域的研究。代数几何本身是现代数学最古老的部分之一，但在过去四分之一个世纪里得到了革命性的发展。在它的起源中，它处理可以通过最简单的方程（即多项式）在平面上定义的图形。如今，该领域不仅使用代数方法，还使用分析和拓扑方法，相反，它正在这些领域以及物理学、理论计算机科学和机器人技术中得到应用。 ***