Workshop on Equivariant Gromov-Witten Theory and Symplectic Vortices; July 2009, Luminy, France

等变 Gromov-Witten 理论和辛涡流研讨会；

• 批准号: 0835558
• 负责人: Christopher Woodward
• 金额: $ 2.51万
• 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: 2008
• 资助国家: 美国
• 起止时间: 2008-10-01 至 2009-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0835558&HistoricalAwards=false
• 关键词: Workshop; Equivariant; Gromov; Witten; Theory

AbstractAward: DMS-0835558Principal Investigator: Christopher WoodwardAlgebraic geometry, symplectic geometry and low-dimensionaltopology have been revolutionized in recent years by theintroduction of holomorphic curve techniques. This workshop, tobe held July 6-10, 2009, at the CIRM (Luminy) conference center,concerns equivariant generalizations of invariants defined byholomorphic curves. In Gromov-Witten theory, equivariantinvariants have been extensively studied by Givental and others,in the sense of integrals of equivariant cohomology classes overmoduli spaces of stable maps. The focus of the workshop will beon the following more sophisticated version of equivariantGromov-Witten theory: the study of moduli spaces of maps to thestack-theoretic quotient of, say, a smooth projective variety bya reductive group. By definition, such a map consists of aholomorphic principal bundle, together with a section of theassociated bundle. From the symplectic point of view, suitablemoduli spaces of such pairs are known as moduli spaces of {\emsymplectic vortices}. The workshop is organized around thisspecific direction, with an aim to bring together researchers inalgebraic and symplectic geometry who have had no previousinteraction. On the other hand, the workshop will promotediscussion of the interaction of holomorphic maps, gauge theory,and group actions more broadly. Applications of the theory areexpected for instance, to the relation between Gromov-Wittentheories of different varieties, and to the relation between thegauge-theoretic invariants such as Floer-Donaldson invariants andtheir symplectic analogs.We propose a workshop which will bring together gauge theory andholomorphic curves. Gauge theory is the study of local symmetryin mathematics and physics; the most famous example iselectromagnetism. Holomorphic curve techniques aim, in algebraicgeometry, to understand spaces by understanding the certainclasses of curves in them, or in symplectic geometry, tounderstand the periodic orbits of dynamical systems. Symmetry ofthe target varieties may be used as a computational tool, andalso combined with holomorphic curves to define new invariants.The workshop will focus on recent developments and emergingapplications to algebraic geometry, symplectic geometry, andlow-dimensional topology. The workshop will benefit a number ofgraduate students and postdoctoral fellows working in this areawho have had little interaction with other groups working onrelated problems.The conference web-page controlled by the organizers iswww.math.rutgers.edu/~ctw/Luminy, while that controlled by theconference center CIRM iswww.cirm.univ-mrs.fr/web.ang/liste_rencontre/Rencontres2009/Renc346/Renc346.html.

Abstractaward：DMS-0835558原理研究者：近年来，Christopher Woodwardalgebraic的几何形状，符号几何形状和低维度学因霍明态曲线技术的引入而彻底改变了。 该研讨会于2009年7月6日至10日在CIRM（Luminy）会议中心举行，涉及不变的概括定义的造影曲线的概括。 在格罗莫夫（Gromov-Witten）理论中，吉维尔（Givartent）和其他人对稳定地图的超模型空间的积分阶层进行了广泛的研究。 研讨会的焦点将成为以下更复杂的EquivariantGromov-Witten理论：对图的模量空间的研究，例如，平滑的投射性变体bya还原群体。 根据定义，该地图由Aholomormormormormormormormormormormormormormormormormormormormormormormortal束，以及一部分相关的捆绑包。从符号的角度来看，这种对的适合ablemoduli空间被称为{\ emsympletectic涡流的模量空间}。 该研讨会是围绕这个特定方向组织的，目的是将没有以前的互动的研究人员组合在一起。 另一方面，研讨会将更广泛地促进塑态图，仪表理论和群体行动的相互作用的讨论。 该理论的应用指出，例如，不同品种的gromov-thittentheories之间的关系，以及诸如浮点数不变式等高古理论不变性之间的关系。我们提出了一个研讨会。 量规理论是对局部对称素数学和物理学的研究。最著名的例子Iselectromagnetism。 全体形态曲线技术的目的是在代数地理中，以理解它们的某些曲线曲线或在符号几何形状中来理解空间，而Toundersterster构成了动态系统的周期性轨道。 目标品种的对称性可以用作计算工具，AndoLSO与全体形态曲线结合在一起，以定义新的不变性。该研讨会将重点放在最近的发展和新兴申请上，以实现代数几何，符号几何形状，象征性几何形状，和low-low-dimensionalitional topology。 该研讨会将使在该地区工作的许多研究生和博士后研究员受益于与其他相关问题的小组互动。 iswww.cirm.univ-mrs.fr/web.ang/liste_rencontre/rencontres2009/renc346/renc346.html。