Mirror Symmetry and Modular Functions

镜像对称和模函数

• 批准号: 9619884
• 负责人: Bong Lian
• 金额: $ 7.4万
• 依托单位: Brandeis University
• 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 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9619884&HistoricalAwards=false
• 关键词: Mirror; Symmetry; Modular; Functions

Lian 9619884 This research is concerned with work on mirror symmetry and modular functions. The principal investigator will work on extending known results for toric hypersurfaces to the case of toric complete intersections. He will try to construct all large radius limit points. He will also work on extending work on modularity of the mirror map for K3 surfaces to arbitrary 1-parameter families and to multiparameter families. Finally, he will study S-duality for K3-fibered threefolds. 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.

Lian 9619884本研究是关于镜像对称和模函数的工作。首席研究员将致力于将环面超曲面的已知结果扩展到环面完全相交的情况。他将尝试构造所有大半径极限点。他还将致力于扩展K3曲面的镜像映射的模块化到任意1参数族和多参数族的工作。最后，他将研究k3纤维三层的s对偶性。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。