Functoriality in Gromov-Witten Theory and Beyond

格罗莫夫-维滕理论及其他理论中的函数性

• 批准号: 1162590
• 负责人: Yuan-Pin Lee
• 金额: $ 28.15万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1162590&HistoricalAwards=false
• 关键词: Functoriality; Gromov; Witten; Theory; Beyond

The proposed research lies on the interaction between algebraic geometry and mathematical physics. Specifically, it concerns the Gromov-Witten (GW) theory and variation of Hodge structures (VHS) on one side and birational geometry, algebraic cobordism, and mirror symmetry on the other. The main themes of the proposal are the functoriality of GW theory under crepant transformations and the extended functoriality of GW and VHS under extremal transitions (also known as space-time topology change in the physics literature). Gromov-Witten theory lies in the intersection of many exciting research areas in mathematics and physics. On the one hand, the theory itself has remarkable structures, both established and conjectural. Investigating these structures requires some new insights and technical tools and input from other areas. This provides a lot of interesting problems for classical subjects in mathematics. On the other hand, these new insights and technical tools help to discover deep relations and connections between existing mathematics and theoretical physics, especially the topological string theory.

拟议的研究在于代数几何和数学物理之间的相互作用。具体来说，它一方面涉及格罗莫夫-维滕 (GW) 理论和霍奇结构 (VHS) 的变分，另一方面涉及双有理几何、代数共边和镜像对称。该提案的主题是 GW 理论在 Crepant 变换下的函子性以及 GW 和 VHS 在极值跃迁下的扩展函子性（在物理文献中也称为时空拓扑变化）。 格罗莫夫-维滕理论是数学和物理学中许多令人兴奋的研究领域的交叉点。一方面，该理论本身具有显着的结构，既有已成立的结构，也有推测的结构。研究这些结构需要一些新的见解和技术工具以及其他领域的投入。 这为数学中的经典学科提供了许多有趣的问题。另一方面，这些新的见解和技术工具有助于发现现有数学和理论物理，特别是拓扑弦理论之间的深层关系和联系。