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.