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.

拟研究的内容是Gromov-维滕理论与其他数学和物理学科之间的相互作用，包括双有理几何、曲线模和镜像对称。该提案的主题是函数的Gromov-维滕理论下的crepant transformations和镜像对称orbifold categories.Gromov-维滕理论是在许多令人兴奋的研究领域在数学和物理学的交叉点。一方面，该理论本身具有显著的结构性特征。研究这些结构需要对理论和其他领域的投入有一些新的见解。这为数学中的经典学科提供了许多有趣的问题。另一方面，它也有助于发现现有数学之间的深层关系和联系。