Mathematical Sciences: Research Proposal in Algebraic Geometry

数学科学：代数几何研究计划

• 批准号: 9503249
• 负责人: Ron Donagi
• 金额: $ 7.46万
• 依托单位: University of Pennsylvania
• 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: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503249&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Proposal; Algebraic

9503249 Donagi Professor Donagi will study problems that derive from the interaction of algebraic geometry with the theory of integrable systems. In particular, he will study mirror symmetry, normal functions of curves in their Jacobians, the geometpic Langlands conjecture and the compatibility of connections of non-abelian theta functions with an abelianized version. This is research in the field of algebraic geometry, yet it directly connects to two of the great advances in theoretical physics in this century--quantum mechanics and general relativity. Algebraic geometry itself 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9503249 Donagi教授将研究从代数几何与可积系统理论的相互作用中产生的问题。特别是，他将研究镜像对称，正常职能的曲线在其雅可比，geometpic朗兰兹猜想和兼容性的连接非阿贝尔θ函数与abelianized版本。 这是代数几何领域的研究，但它直接关系到本世纪理论物理学的两个重大进展--量子力学和广义相对论。代数几何本身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。 ***