Mathematical Sciences: Geometric Conformal Field Theories, Mirror Symmetry, and Algebraic Geometry

数学科学：几何共形场论、镜像对称和代数几何

• 批准号: 9401447
• 负责人: David Morrison
• 金额: $ 21万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401447&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Conformal; Field

Professor Morrison will work on research on the border between theoretical physics and algebraic geometry. He will use algebraic geometric techniques to study conformal field theory. In particular he intends to further study the recently discovered phenomenon of mirror symmetry. 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.

莫里森教授将致力于理论物理和代数几何之间的边界研究。他将使用代数几何技术来研究共形场理论。特别是，他打算进一步研究最近发现的镜面对称现象。这是代数几何领域的研究，但它与本世纪理论物理的两大进步--量子力学和广义相对论--直接相关。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25年里，它已经取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。