Non-Abelian Hodge Theory and Applications

非阿贝尔霍奇理论及其应用

• 批准号: 9700605
• 负责人: Ludmil Katzarkov
• 金额: $ 9.15万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-15 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9700605&HistoricalAwards=false
• 关键词: Non; Abelian; Hodge; Theory; Applications

Katzarkov 9700605 This project supports work on three problems on non-abelian Hodge theory and its applications. The first problem is concerned with work on the Shafarevich conjecture. The principal investigator will work on non-abelian analogs of the theorems of the (p,p) cycles, of the fixed pard theorem, and of the nonabelian Clemens Schmidt sequence. The second problem concerns a study of algebraic cycles on algebraic surfaces. The principal investigator will use the action of a certain infinite dimensional Heizenberg algebra on the kernel of the Albanese map to try to prove the Bloch conjecture. The third problem concerns work on families of K3 surfaces. 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.

卡察尔科夫9700605 该项目支持非阿贝尔霍奇理论及其应用的三个问题的工作。 第一个问题是关于Shafarevich猜想的工作。 主要研究人员将致力于非阿贝尔类似物的定理的（p，p）周期，固定帕德定理，和nonabelian克莱门斯施密特序列。 第二个问题是关于代数曲面上的代数圈的研究。 主要研究者将利用某个无穷维海森堡代数对Albanese映射核的作用来尝试证明Bloch猜想。 第三个问题涉及K3曲面族的工作。 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个世纪里，它已经有了革命性的发展。 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。