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首席研究员：Eleny-Nicoleta Ionel第一个项目的目标是获得标记黎曼曲面上复杂结构的模空间的上同调中的新关系。 使用她早期工作中开发的技术，PI发现了几个有趣的关系，其中一个可以证明关于thetautological环生成元的Faber猜想。第二个项目试图找到相对和绝对Gromov-Witten不变量之间的关系。 这样的关系似乎是有用的镜像猜想计算，以及在其他几个开放的问题在枚举几何。最后的项目提出了两种方法来扩展theGromov类型的不变量，以“非通用”的情况。 这将提供关于辛流形的更精确的信息。 枚举代数几何中的大多数问题都有一百多年的历史了。这些问题很容易提出来，但用经典方法解决这些问题的进展却相当缓慢。近年来，在高能物理的二维拓扑量子场论中也出现了类似的问题。在这些理论的启发下，新的方法在过去几年中在该领域取得了惊人的进展。 该方案探索了两条新的途径来解决这些老问题，这将进一步阐明二维拓扑量子场论的结构。