Gromov--Witten theory and its relations with moduli of curves, birational geometry, K-theory and orbifold mirror symmetry

格罗莫夫--维滕理论及其与曲线模量、双有理几何、K理论和轨道镜像对称的关系

• 批准号: 0600688
• 负责人: Yuan-Pin Lee
• 金额: $ 10.85万
• 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: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600688&HistoricalAwards=false
• 关键词: Gromov; Witten; theory; its; relations

The proposed research deals with the interaction between Gromov--Witten theoryand other subjects in mathematics and physics, including birational geometry,moduli of curves, K-theory, integrable systems, and mirror symmetry.Some of the main problems investigated are:the structure of the tautological rings,quantum cohomology under birational transformations,Virasoro symmetries,and orbifold mirror symmetry.Gromov--Witten theory lies in the intersection of many exciting researchareas in mathematics and physics.On the one hand, the theory itself has some remarkable conjectural structures.Proof of these conjectures and discovery of new ones will require somenew insights into the theory and input from other areas.On the other hand, it has also provided many powerful ideas and deepconnections in many directions from string theory to classical subjects inmathematics.Some of these ideas and connections will be explored in this proposal.

所提出的研究涉及格罗莫夫-维滕理论与数学和物理中其他学科之间的相互作用，包括双有理几何、曲线模、K理论、可积系统和镜像对称。研究的一些主要问题是：同义反复环、双有理变换下的量子上同调、维拉索罗对称性和轨道镜像对称性。格罗莫夫-维滕理论位于许多令人兴奋的研究领域的交叉点一方面，该理论本身具有一些显着的猜想结构。这些猜想的证明和新猜想的发现将需要对该理论的一些新见解和其他领域的输入。另一方面，它也提供了许多从弦理论到数学经典学科，在许多方向上都有强有力的思想和深刻的联系。本提案将探讨其中一些思想和联系。