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.

摘要奖项：DMS-0835558 首席研究员：Christopher Woodward 近年来，由于全纯曲线技术的引入，代数几何、辛几何和低维拓扑发生了革命性的变化。 该研讨会将于 2009 年 7 月 6 日至 10 日在 CIRM (Luminy) 会议中心举行，讨论全纯曲线定义的不变量的等变推广。 在 Gromov-Witten 理论中，Givental 等人在稳定映射的等变上同调类超模空间积分的意义上对等变不变量进行了广泛的研究。 研讨会的重点将是等变格罗莫夫-维滕理论的以下更复杂的版本：研究映射的模空间到堆栈理论商，例如由约简群的平滑射影簇。 根据定义，这样的映射由全纯主丛以及相关丛的一部分组成。从辛的角度来看，此类对的合适模空间称为{\emsymplectic vortices}的模空间。 该研讨会是围绕这个特定方向组织的，旨在将以前没有互动过的代数和辛几何研究人员聚集在一起。 另一方面，研讨会将促进更广泛地讨论全纯映射、规范理论和群体行为的相互作用。 例如，该理论的应用有望应用于不同类型的 Gromov-Witten 理论之间的关系，以及规范理论不变量（例如 Floer-Donaldson 不变量及其辛类似物）之间的关系。我们提出了一个将规范理论和全纯曲线结合在一起的研讨会。 。 规范理论是数学和物理学中局部对称性的研究；最著名的例子是电磁学。 在代数几何中，全纯曲线技术的目标是通过理解空间中的某些曲线来理解空间，或者在辛几何中，全纯曲线技术的目标是理解动力系统的周期轨道。 目标品种的对称性可以用作计算工具，也可以与全纯曲线相结合来定义新的不变量。研讨会将重点关注代数几何、辛几何和低维拓扑的最新发展和新兴应用。 该研讨会将使许多在该领域工作的研究生和博士后受益，他们与其他研究相关问题的小组很少有互动。组织者控制的会议网页是www.math.rutgers.edu/~ctw/Luminy，而由会议中心 CIRM 控制是www.cirm.univ-mrs.fr/web.ang/liste_rencontre/Rencontres2009/Renc346/Renc346.html。