Recursive formulas for Gromov-Witten invariants

Gromov-Witten 不变量的递归公式

• 批准号: 0071393
• 负责人: Eleny-Nicoleta Ionel
• 金额: $ 5.87万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-01 至 2003-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071393&HistoricalAwards=false
• 关键词: Recursive; formulas; Gromov; Witten; invariants

Award: DMS-0071393Principal Investigator: Eleny-Nicoleta IonelThe goal of the first project is to obtain new relations in thecohomology of the moduli space of complex structures on a markedRiemann surface. Using techniques developed in her earlier work,the PI found several interesting relations, one of which couldprove the Faber conjecture about the generators of thetautological ring. The second project seeks to find relationsbetween the relative and absolute Gromov-Witten invariants. Suchrelations appear to be useful in mirror conjecture computations,as well as in several other open problems in enumerativegeometry. The final project suggests two ways of extending theGromov-type invariants to `nongeneric' situations. This wouldprovide more refined information about the symplectic manifold. Most of the problems in enumerative algebraic geometry are morethan a hundred years old. The questions are easy to ask, but theprogress in solving them using classical methods has been quiteslow. Recently, the same kind of questions arised in twodimensional topological quantuum field theories from high energyphysics. Inspired by these theories, new methods lead in the pastcouple of years to amazing progress in the field. The proposalexplores two new ways of approaching these old problems thatwould further clarify the structure of the two dimensionaltopological quantuum field theories.

奖项：DMS-0071393原理研究者：Eleny-Nicoleta ionelta ionel的目标是在Markedriemann表面上获得复杂结构的模量空间的新关系。 PI使用她早期的工作中开发的技术，发现了几个有趣的关系，其中一种可以使Faber猜想有关thetautologicy环的发电机。第二个项目旨在在相对和绝对的格罗莫夫 - 宽容不变的人之间找到关系。 这种关联似乎在镜像猜想计算以及枚举地理测定法中的其他几个开放问题中很有用。最终项目提出了将gromov型不变性扩展到“非古纳尼尔”情况的两种方法。 这将提供有关符号歧管的更多精致信息。 枚举代​​数几何形状的大多数问题是一百年历史的。这些问题很容易提出，但是使用经典方法解决问题的过程已经疑惑。最近，来自高能量物理学的二维拓扑量化场理论中出现了同样的问题。受这些理论的启发，新方法在过去的年度中导致了该领域的惊人进步。 PropoSalexPlose解决了这些旧问题的两种新方法，将进一步阐明二维Quantuum田间理论的结构。