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: 0904653
• 负责人: Zhiqin Lu
• 金额: $ 26.49万
• 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: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0904653&HistoricalAwards=false
• 关键词: Geometry; Calabi; Yau; Moduli; Kahler

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The 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. The proposer will also generalize the Tian--Yau--Zelditch expansion, study the spectrum problem of quantum layers.The work of the proposer is related to string theory, which is a developing branch of theoretical physics that combines quantum mechanics and general relativity into a quantum theory of gravity.Using differential geometry, he solves problems posed by string theorists. He will continue work in the differential geometric aspects of string theory. The proposer is also involved in many educational activities such as the California Math Counts Program, the UCI Anteater Math Club, the UCI School of Physical Sciences Mentor Program, etc. Currently, he is the UCI math department undergraduate student adviser, and is involved in the innovation of both undergraduate and graduate studies. 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.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。这个建议的目的是继续研究微分几何和相关领域的几个基本问题。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。 他的工作与弦理论有关，弦理论是理论物理学的一个发展中的分支，它将量子力学和广义相对论结合成一个量子引力理论。他利用微分几何解决了弦理论家提出的问题。他将继续工作的微分几何方面的弦理论。提议人还参与了许多教育活动，如加州数学计数计划，UCI食蚁兽数学俱乐部，UCI物理科学学院导师计划等，目前，他是UCI数学系本科生顾问，并参与本科和研究生学习的创新。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。