Moduli Spaces Relative Singular Divisors and Lagrangians

奖项：dms -0905738首席研究员：Eleny ionel该奖项由2009年美国复苏与再投资法案（公法111-5）资助。该建议旨在通过结合几个不同研究领域的思想来增加对稳定全纯映射模空间结构的理解。该项目的核心是寻求使用几何和分析方法来研究在某些自然退化过程中这些模会发生什么。特别地，它导致了定义Gromov-Witten不变量相对于特定类型的奇异子空间的厌恶性，包括相对于正规交叉辛除数和以规定方式相交的拉格朗日。它还研究了这些不变量在环境空间或除数和拉格拉格量的适当平滑下的表现。提出的工作是弦理论和辛拓扑的交叉。弦理论作为统一广义相对论和粒子物理学的潜在候选者而发展起来。这个理论的细节被证明是非常丰富的，并在数学上激发了许多显著的结果。但数学的结果也指导和启发了弦理论和镜像对称的许多新发现。希望这个项目将有助于促进数学和其他科学各个领域之间日益增长的互动。特别地，贯穿这一提议的主题之一是辛拓扑可以为弦理论提供见解。

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.