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

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。本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。推广Tian—Yau—Zelditch展开，研究量子层的谱问题。该提议者的工作与弦理论有关，弦理论是理论物理学的一个发展分支，它将量子力学和广义相对论结合成引力的量子理论。利用微分几何，他解决了弦理论家提出的问题。他将继续研究弦理论的微分几何方面。申请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数学系的本科生指导老师，并参与了本科生和研究生学习的创新。他将通过演讲和指导学生，向学生和公众传达他的数学见解。他将继续鼓励更多的人，尤其是女性和少数民族，学习数学。

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.