Gauged Gromov-Witten theory and holomorphic quilts

计量格罗莫夫-维滕理论和全纯被子

• 批准号: 0904358
• 负责人: Christopher Woodward
• 金额: $ 40.19万
• 依托单位: Rutgers University New Brunswick
• 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: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0904358&HistoricalAwards=false
• 关键词: Gauged; Gromov; Witten; theory; holomorphic

AbstractAward: DMS-0904358Principal Investigator: Christopher WoodwardThe PI will carry out projects on functoriality for Lagrangiancorrespondences in Fukaya-Floer theory and functoriality for quotientsin Gromov-Witten theory. The first group of projects will haveapplications in Gromov-Witten theory and ``cohomological'' mirrorsymmetry, that is, in the sense of Givental etc. With F. Ziltener andhis former postdoctoral advisee E. Gonzalez he will investigatefunctoriality for Gromov-Witten invariants under the symplecticquotient construction. Potential applications include invariance ofGromov-Witten invariants under symplectic birational equivalence, tocohomological mirror symmetry for complete intersections of generaltype. With K. Wehrheim and his former student S. Mau the PI willstudy functoriality of Lagrangian correspondences in Floer-Fukayatheory. Applications include symplectic definitions of non-abelianFloer homology for tangles and arbitrary three-manifolds, possiblegeneralizations of Khovanov homology and categorification of quantumgroups. These projects will have applications in homological mirrorsymmetry and low-dimensional topology. Some of the projects have agraduate education component, and the PI also proposes severalundergraduate research projects.Overall the research carried out under this grant will advance theunderstanding of symplectic geometry, which is the mathematicallanguage for classical dynamical systems, and the relationship betweengauge theory, representation theory, and quantum physics. Gaugetheories arise naturally in a number of physical settings, such aselectromagnetism. The first part of the project concerns certaingauge theories with an addition "non-linear" field taking values in aclassical phase space, which have been substantially studied in thephysics literature in the linear case under the name "gauged sigmamodels". The second part of the project concerns the structuralproperties of "Floer-theoretical" invariants which have beenextensively studied in relation to dynamical systems in recent years.

Abstractaward：DMS-0904358原理研究者：Christopher Woodwardththe Pi将在福卡亚 - 弗洛伊尔理论中进行有关Lagrangian-Corresporce的功能性项目，并实现Gromov-Witter理论的商人的功能。 第一组项目将在gromov-witten理论和``共同体学''镜像中进行，即在志愿意义上等。与F. Ziltener和F. Ziltener Andhis Andhis Postdoctoral Andhis E. Gonzalez一起，他将调查Gromov-Witter-Witter-Witter-Witter-Witter-witchoriality interplectimplectimplectemplectemplectimplecticquicquicquicquicqueqicquicquqicquicquicquqicquicquqicquicquqicquicqueqicequqicequeqien consements。 潜在的应用包括在象征性的异性等效性下的gromov-onginten不变性，对于通用类型的完整交集的酒精学镜像对称性。 K. Wehrheim和他的前学生S. Mau在Floer-Fukayatheory中的Lagrangian对应关系的Pi WillStudy功能性。 应用包括对缠结和任意三个manifolds的非阿贝里安弗洛勒同源性的符合性定义，khovanov同源性的可能构造和量子组的分类。 这些项目将在同源镜像和低维拓扑中应用。 其中一些项目具有农业教育部分，PI还提出了几项研究生研究项目。毕竟，根据该赠款进行的研究将推动对符号几何形状的理解，这是经典动力学系统的数学语言，以及Gauge理论，表示理论和量化物理学之间的关系。 仪表自然出现在许多物理环境中，例如海磁性。 该项目的第一部分涉及Certaingauge的理论，并具有一个添加的“非线性”字段，在典型的相位空间中采用了值，在线性案例中，该阶段的价值是在线性文献中进行了大量研究的，名称为“测量sigmamamodels”。 该项目的第二部分涉及近年来与动态系统有关的“浮动理论”不变性的结构性专业。