On the Geometry of Calabi-Yau Moduli and Kahler-Einstein manifolds

论卡拉比-丘模数和卡勒-爱因斯坦流形的几何

• 批准号: 1206748
• 负责人: Zhiqin Lu
• 金额: $ 16.5万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-15 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1206748&HistoricalAwards=false
• 关键词: Geometry; Calabi; Yau; Moduli; Kahler

AbstractAward: DMS 1206748, Principal Investigator: Zhiqin LuThe object of this proposal is to continue to study several fundamental problems in differential geometry and related fields. The long-term goal is to study the higher order BCOV conjecture and relations between the existence of Kahler-Einstein metrics and the stability of complex manifolds. One of the short-term goals is to study the different notations of stability. In particular, the proposer will study the relations between the Donaldson-Futaki invariant and the Tian-Futaki invariant. The proposer believes that, like the Futaki invariant, both invariants are combinatorial. He will also generalize the Tian-Yau-Zelditch expansion, study the gap problem, study the spectral problem of quantum layers, and study some fundamental linear algebra problems related to the mean curvature flow.The proposed problems are important in differential geometry and mathematical physics. It has significant impacts in our understanding of the Universe. As before, he will convey his mathematical insights to students and to the general public by giving talks and advising students. He will continue to encourage more people, especially women and minorities, to study mathematics. To achieve the goal, the proposer is involved in many educational activities such as the California Math Counts, the UCI Anteater Math Club, the UCI School of Physical Sciences Mentor Program, etc. He is involved in the innovation of both undergraduate and graduate courses.

AbstractAward：DMS 1206748，主要研究员：路志勤本提案的目的是继续研究微分几何及其相关领域中的几个基本问题。长期目标是研究高阶BCOV猜想以及Kahler-Einstein度量的存在性与复流形稳定性之间的关系。短期目标之一是研究稳定性的不同符号。特别地，提出者将研究Donaldson-Futaki不变量和Tian-Futaki不变量之间的关系。提出者认为，像Futaki不变量一样，这两个不变量都是组合的。他还将推广Tian-Yau-Zelditch展开，研究差距问题，研究量子层的谱问题，研究与平均曲率流相关的一些基本线性代数问题，提出的问题在微分几何和数学物理中具有重要意义。它对我们对宇宙的理解产生了重大影响。和以前一样，他将通过演讲和为学生提供建议，向学生和公众传达他的数学见解。他将继续鼓励更多的人，特别是妇女和少数民族，学习数学。为了实现这一目标，提案人参与了许多教育活动，如加州数学计数，UCI食蚁兽数学俱乐部，UCI物理科学学院导师计划等，他参与了本科和研究生课程的创新。