Mathematical Sciences: Moduli Problems in Algebraic Geometry

数学科学：代数几何中的模问题

• 批准号: 9500964
• 负责人: Michael Thaddeus
• 金额: $ 4.5万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500964&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Moduli; Problems; Algebraic

9500964 Thaddeus Professor Thaddeus will study the topology and geometry of quotient varieties using his techniques of flips. In particular he will study configuration spaces of certain projective spaces. He will also study moduli spaces off vector bundles and curves. he hopes to compute relations in their cohomology rings and the associated Hilbert polynomials. 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. ***

9500964 Thaddeus教授Thaddeus将使用他的翻转技术研究商的拓扑和几何形状。特别是他将研究某些投影空间的配置空间。 他还将研究矢量束和曲线的模量空间。 他希望在他们的共同体戒指和相关的希尔伯特多项式中计算关系。 这是代数几何学领域的研究，但它直接连接到本世纪理论物理学的两个巨大进步 - 量子力学和一般相对论。代数几何本身就是现代数学最古老的部分之一，但在过去的25年中，它具有革命性的开花。它起源于它处理的数字可以通过最简单的方程（即多项式）在平面中定义的数字。如今，该领域不仅利用了来自代数的方法，还利用了分析和拓扑的方法，相反，在这些领域以及物理，理论计算机科学和机器人技术中找到了应用。 ***