Mathematical Sciences: Moduli of Manifolds with Canonical Class Zero

数学科学：规范零类流形的模

• 批准号: 9400794
• 负责人: Andrey Todorov
• 金额: $ 6万
• 依托单位: University of California-Santa Cruz
• 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: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400794&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Moduli; Manifolds; Canonical

Professor Todorov will work on the geometry and topology of Calabi-Yau manifolds and K3 surfaces. In particular he wants to work on the Teichmuller theory and the analytic discriminant of Calabi-Yau manifolds. He also wants to study the Krotweg de Vries equation. 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.

Todorov教授将研究Calabi-Yau流形和K3曲面的几何和拓扑。他特别想研究Teichmuller理论和Calabi-Yau流形的解析判别。他还想研究kroweg de Vries方程。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大进步——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个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它在这些领域以及物理学、理论计算机科学和机器人技术中也得到了应用。