Mathematical Sciences: Analytic Geometry and Arithmetic Groups

数学科学：解析几何和算术群

• 批准号: 9002116
• 负责人: John Millson
• 金额: $ 5.96万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002116&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytic; Geometry; Arithmetic

This award supports the research in deformation theory and arithmetic groups of Professor John Millson of the University of Maryland at College Park. Dr. Millson has proposed to work in two main areas: first, he will apply the methods of rational homotopy theory to deformation problems in algebraic geometry; and second, he will continue his research on the cohomology of discrete subgroups of orthogonal and unitary groups. 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 physics, theoretical computer science, and robotics.

该奖项支持变形理论的研究， 约翰·米尔森教授的算术群 马里兰州的学院公园。米尔森博士提议在两个 主要研究领域：首先，他将应用有理同伦的方法 代数几何中变形问题的理论;第二， 他将继续他的研究上同调离散 正交群和酉群的子群 这是代数几何领域的研究， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，革命性的开花。在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。如今，该领域 不仅使用代数方法，而且使用分析方法， 拓扑学，反过来说， 以及物理学、理论计算机科学， 机器人