Moduli Spaces Relative Singular Divisors and Lagrangians

模空间相对奇异因数和拉格朗日

• 批准号: 0905738
• 负责人: Eleny-Nicoleta Ionel
• 金额: $ 65.5万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905738&HistoricalAwards=false
• 关键词: Moduli; Spaces; Relative; Singular; Divisors

AbstractAward: DMS-0905738Principal Investigator: Eleny IonelThis award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The proposal is aimed at increasing understanding of thestructure of the moduli spaces of stable holomorphic maps bycombining ideas from several different fields of research. Thecore of the project seeks to use geometric and analytical methodsto investigate what happens to these moduli during certainnatural degenerations. In particular it leads to defining aversion of Gromov-Witten invariants relative certain type ofsingular subspaces, including relative both a normal crossingsymplectic divisor and a Lagrangian intersecting in a prescribedway. It also investigates how these invariants behave underappropriate smoothings of either the ambient space or of thedivisor and the Lagragian.The proposed work lies at the intersection of string theory andsymplectic topology. String theory developed as a potentialcandidate for unifying general relativity and particlephysics. The details of this theory have turned out to beextraordinarily rich, and have inspired many remarkable resultsin mathematics. But results in mathematics have also guided andinspired many new discoveries in string theory and mirrorsymmetry. It is hoped that this project will contribute to thegrowing interaction between various fields of mathematics andother sciences. In particular, one of the themes running throughthis proposal is that symplectic topology can contribute insightsinto string theory.

Abstractaward：DMS-0905738原理研究者：Eleny Ionelthis Award是根据2009年的《美国回收和再投资法》（公法111-5）资助的。该提案旨在增加对稳定的全体形态图的模量空间的理解，从几个不同的研究领域中撤消思想。该项目的范围试图使用几何和分析方法，研究在某些自然变性过程中这些模量会发生什么。特别是，它导致定义gromov-inting不变性的厌恶相对某些类型的单个子空间，包括相对的正常杂交除法和在处方线中相交的lagrangian。 它还研究了这些不变的人如何表现不适当的环境空间或thedivisor和lagragian的平滑性。拟议的工作在于弦理论和截面拓扑的交集。弦理论发展为统一一般相对论和粒子物理学的潜在范围。事实证明，该理论的细节非常丰富，并激发了许多在数学中的显着结果。但是数学的结果也指导了弦理论和镜像对称性中的许多新发现。希望该项目将有助于数学和其他科学领域之间的增长互动。特别是，通过此建议的主题之一是，符号拓扑可以促进洞察力理论。