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)提供资金的。这项建议的目的是继续研究微分几何及其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度规的存在和复流形的稳定性之间的关系。短期目标之一是研究稳定的不同含义。提出者还将推广田-尤-泽尔迪奇展开，研究量子层的谱问题。提出者的工作与弦理论有关，弦理论是理论物理的一个新兴分支，它将量子力学和广义相对论结合到量子引力理论中。他利用微分几何解决弦理论家提出的问题。他将继续弦理论的微分几何方面的工作。他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物理学院导师计划等。目前，他是UCI数学系本科生顾问，并参与了本科生和研究生的创新。他将通过演讲和给学生提供建议来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。

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.