Mathematical Sciences: Hodge Theory, L 2-Cohomology and Intersection Homology

数学科学：Hodge 理论、L 2-上同调和交交同调

• 批准号: 9423689
• 负责人: Steven Zucker
• 金额: $ 6.98万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9423689&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hodge; Theory; Cohomology

9423689 Zucker Professor Zucker will study locally symmetric spaces via methods of algebraic geometry. In particular he wants to study the relationship between various Hodge structures and cohomology of a locally symmetric variety. He will also study extensions of intersection cohomology to a class of real analytic varieties with a view to proving a version of the decomposition theorem. This is research in the field of algebraic geometry. Algebraic geometry 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. ***

小行星9423689 Zucker教授将通过代数几何的方法研究局部对称空间。特别是他想研究各种霍奇结构和上同调的局部对称品种之间的关系。他还将研究扩展交叉上同调一类真实的分析品种，以期证明一个版本的分解定理。 这是代数几何领域的研究。代数几何是现代数学中最古老的部分之一，但在过去的四分之一世纪中却有了革命性的发展。在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。 如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，这些方法在这些领域以及物理学，理论计算机科学和机器人学中也得到了应用。 ***