Gromov-Whitten Theory and its Relations With K-Theory, Integrable Systems and Enumerative Geometry

Gromov-Whitten 理论及其与 K 理论、可积系统和枚举几何的关系

• 批准号: 0072547
• 负责人: Yuan-Pin Lee
• 金额: $ 8.13万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072547&HistoricalAwards=false
• 关键词: Gromov; Whitten; Theory; its; Relations

DMS-0072547Yuan-Pin LeeQuantum cohomology is a deformation of usual cup productof ordinary cohomology ring of a smooth projective variety X. Similarly quantum K-theory is a deformation of ordinary K-ring of X. In their study of Gromov--Witten K-theory, Professor Lee and his collaborators have found some interesting relations to other fields in mathematics and physics including algebraic geometry, integrable systems, representation theory and quantum geometry. These investigations also naturally lead to further investigations of Gromov--Witten theory itself. The main focus of this project will be on quantum cohomology, quantum K-theory and their relations to discrete KdV hierarchies, Toda lattices, and enumerative geometry. Gromov-Witten theory is a new subject that lies within theintersection of many traditional branches of mathematics and theoretical physics. This theory was originally discovered within string theory. Shortly thereafter people found many new applications to mathematics. Some of these applications solvedproblems that, based on traditional methods, were considered tobe very difficult. The tools used to study Gromov--Witten theory also involves many fields, including algebraic geometry, topology and analysis. Thus, this is a growing new field which exhibits many rich structures and deserves further investigation

DMS-0072547 Yuan-pin Leequantum coomology是对平滑投影品种的常规杯子产物的变形。类似地，量子K理论是X的普通k-ring的变形。可集成的系统，表示理论和量子几何形状。 这些研究也自然会导致对格罗莫夫（Gromov）的进一步研究 - 理论本身。 该项目的主要重点将放在量子共同体，量子K理论及其与离散的KDV层次结构，Toda lattices和枚举几何形状的关系上。 Gromov-Witten理论是一个新主题，位于许多传统的数学和理论物理学分支。 该理论最初是在字符串理论中发现的。 此后不久，人们发现了许多新的数学应用程序。 这些应用程序中的一些解决了基于传统方法的问题非常困难。 用于研究Gromov的工具 - 知识理论还涉及许多领域，包括代数几何，拓扑和分析。 因此，这是一个不断增长的新领域，展示了许多丰富的结构并值得进一步研究