Geometry and Topology of Manifolds with Special Holonomy

特殊完整流形的几何与拓扑

• 批准号: 1105663
• 负责人: Sema Salur
• 金额: $ 12.67万
• 依托单位: University of Rochester
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1105663&HistoricalAwards=false
• 关键词: Geometry; Topology; Manifolds; Special; Holonomy

Manifolds with special holonomy and calibrated geometry have important relations with symplectic geometry, complex geometry, algebraic geometry, Cartan-Kahler Theory and Seiberg-Witten Theory. In this project, the P.I. plans to continue her work on calibrated submanifolds of Calabi-Yau, G_2 and Spin(7) manifolds. In joint work with S. Akbulut, the P.I. studied complex associative and complex Cayley submanifolds and using the SW theory she showed that the moduli space of these submanifolds is smooth without any obstructions to such deformations. She also introduced the mathematical definitions of mirror Calabi-Yau and G_2 manifolds. The P.I. plans to continue her work on compactification problems of these moduli spaces and to study the mirror dualities in other Calabi-Yau and G_2 manifolds. These will lead to the construction of new counting invariants and provide a better understanding of the mirror symmetry phenomenon. The research topics of this project are motivated by questions in geometry and topology of low dimensional manifolds and mathematical physics. The P.I. believes that this makes calibrated geometry an excellent subject for students who might decide to study math and science, and as a female researcher in this exciting area she feels a particular responsibility to encourage young women to begin and to continue their studies of mathematics. She will continue to encourage both undergraduate and graduate students and to collaborate with them in this research field which is expected to have a long-lasting impact on both mathematics and physics.

具有特殊完整性和校准几何的流形与辛几何、复几何、代数几何、Cartan-Kahler理论和Seiberg-Witten理论有着重要的联系。在这个项目中，P.I.计划继续研究Calabi-Yau流形、G_2流形和Spin（7）流形的标定子流形。在与S。阿克布卢特那个私家侦探研究复杂的关联和复杂的凯莱子流形和使用SW理论，她表明，模空间的这些子流形是顺利的，没有任何障碍，这种变形。她还介绍了镜像卡-丘流形和G_2流形的数学定义。私家侦探她计划继续研究这些模空间的紧化问题，并研究其他Calabi-Yau流形和G_2流形中的镜像对偶。这将导致新的计数不变量的建设，并提供了一个更好的理解镜像对称现象。本计画的研究主题是由低维流形的几何与拓扑以及数学物理所引发。 私家侦探她认为，这使得校准几何的学生谁可能决定学习数学和科学的一个很好的主题，作为一个女性研究人员在这个令人兴奋的领域，她觉得特别有责任鼓励年轻女性开始，并继续他们的数学学习。她将继续鼓励本科生和研究生，并与他们在这一研究领域，预计将有一个长期的影响数学和物理合作。