Mathematical Sciences: Topics in Algebra and Geometry

数学科学：代数和几何主题

• 批准号: 8901784
• 负责人: Henri Gillet
• 金额: $ 12.22万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901784&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Algebra; Geometry

This award supports the research in K-Theory and Algebraic Geometry of Professor Henri Gillet of the University of Illinois at Chicago. In continuing joint work with C. Soule, he plans to investigate the relationship between algebraic and differential- geometric invariants of arithmetic varieties, and possibly to apply these results to questions in number theory. Another project of Dr. Gillet is to continue joint work with Dr. Peter Shalen in studying the actions of groups on generalized trees, with the idea of using these actions to obtain information about the cohomology of the groups involved. This is research in the field of Algebraic Geometry, 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 theoretical Computer Science and in Robotics.

该奖项支持伊利诺伊大学芝加哥分校教授亨利·吉利特在K理论和代数几何方面的研究。在继续与C.Soule的合作中，他计划研究算术簇的代数不变量和微分几何不变量之间的关系，并可能将这些结果应用于数论中的问题。Gillet博士的另一个项目是继续与Peter Shalen博士合作研究群在广义树上的作用，想法是利用这些作用来获得有关所涉及的群的上同调的信息。这是对代数几何领域的研究，它是现代数学中最古老的部分之一，但在过去的25年里取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，这个领域不仅使用了代数的方法，而且使用了分析和拓扑学的方法，相反，它在这些领域以及理论计算机科学和机器人学中都得到了应用。