Mathematical Sciences: Harmonic Mappings, Discrete Groups, and Hodge Theory

数学科学：调和映射、离散群和霍奇理论

• 批准号: 8907207
• 负责人: James Carlson
• 金额: $ 11.68万
• 依托单位: University of Utah
• 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: 1989-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8907207&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Harmonic; Mappings; Discrete

This award supports the research in Algebraic Geometry of Professors James Carlson and Domingo Toledo of the University of Utah. Their work is in Hodge theory, and their aim is to attack the problem of classifying harmonic mappings from compact Kaehler manifolds to locally symmetric spaces of noncompact type, with particular attention to rigidity and factorization theorems. 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.

该奖项支持在代数几何的研究， 哥伦比亚大学的詹姆斯·卡尔森和多明戈·托莱多教授 犹他州。他们的工作是在霍奇理论，他们的目的是攻击 紧Kaehler调和映射分类问题 流形到非紧型局部对称空间， 特别注意刚性和因式分解定理。 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 使用的方法不仅从代数，但从分析和 拓扑学，反过来说， 以及理论计算机科学和机器人学。