RUI: Moduli Spaces and Combinatorial Algebraic Geometry

RUI：模空间和组合代数几何

• 批准号: 1101625
• 负责人: Linda Chen
• 金额: $ 13.25万
• 依托单位: Swarthmore College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101625&HistoricalAwards=false
• 关键词: RUI; Moduli; Spaces; Combinatorial; Algebraic

The investigator will study various combinatorial and enumerative problems in algebraic geometry. Fundamentally linked to these problems are the study of moduli and parameter spaces and their cohomology theories, the study of objects combinatorially rich in structure, and degeneration techniques and their applications. In particular, the investigator proposes to investigate equivariant quantum cohomology theories, affine Grassmannians, Hessenberg varieties, flag varieties, moduli spaces of curves, quot schemes, GKM spaces, and stacks and their toric degenerations.The proposed research problems are concerned with fruitful interactions between modern methods in algebraic geometry and new developments in combinatorics, symplectic geometry, and physics. The proposed projects have significant potential impact on enhancing the understanding of fundamental objects in algebraic geometry and their connections to one another. Through research, education, advising, and organizing, the investigator will promote interactions and collaborations between students and faculty of colleges and universities.

调查员将研究代数几何中的各种组合和枚举问题。从根本上联系到这些问题是研究模和参数空间及其上同调理论，研究对象组合丰富的结构，退化技术及其应用。特别是，研究者提出研究等变量子上同调理论，仿射Grassmannian，Hessenberg簇，flag簇，曲线的模空间，“方案，GKM空间，栈和它们的环面退化.所提出的研究问题涉及代数几何的现代方法与组合学，辛几何和物理学的新发展之间富有成效的相互作用.拟议中的项目有显着的潜在影响，以提高代数几何的基本对象的理解和它们之间的联系。 通过研究，教育，咨询和组织，调查员将促进学生和高校教师之间的互动和合作。