Functoriality of Gromov--Witten theory

格罗莫夫函数性--维滕理论

• 批准号: 0901098
• 负责人: Yuan-Pin Lee
• 金额: $ 25.33万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901098&HistoricalAwards=false
• 关键词: Functoriality; Gromov; Witten; theory

The proposed research lies on the interaction between Gromov--Witten theory and other subjects in mathematics and physics, including birational geometry, moduli of curves, and mirror symmetry. The main themes of the proposal are the functoriality of Gromov--Witten theory under crepant transformations and the mirror symmetry in the orbifold category.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 conjectural structures. Investigating these structures requires some new insights into the theory and input from other areas. This provides a lot of interesting problems for classical subjects in mathematics. On the other hand, it also helps to discover deep relations and connections between existing mathematics.

拟议的研究在于格罗莫夫（Gromov） - 知识理论与数学和物理学中的其他学科之间的相互作用，包括曲线，曲线模量和镜面对称性。该提案的主要主题是Gromov的功能性 - 在orbifold类别中的毛发转化和镜像对称性下的功能。Gromov-含有理论在于许多数学和物理学中许多令人兴奋的研究领域的交集。一方面，理论本身具有显着的猜想结构。研究这些结构需要对其他领域的理论和投入的一些新见解。这为数学中的古典主题提供了许多有趣的问题。另一方面，它还有助于发现现有数学之间的深厚关系和联系。