CAREER: On the Geometry of Kahler-Einstein Manifolds

题目：职业-关于Kaehler-Einstein流形的几何研究（ei）： Zhiqin Lu （University of California, Irvine）摘要：拟研究某单位圆束的Szego核。这一问题的研究与流形的稳定性密切相关。目前认为流形的稳定性是求解范诺流形上的kaehler - einstein方程的关键概念。另一个问题的提议将涉及几何的calabi - yau模。特别是，calabi - yau模上的BCOV扭转可能在验证镜像对称中的一些预测中起关键作用。申请人将参与各种教育项目以及各种活动，以提高教育效率。提出者正在研究几何学中的一些关键问题，这些问题不仅对数学很重要，而且对物理学等其他科学也很重要。例如，广义相对论是重力的几何理论。提议者工作的一个应用与“允许的”宇宙的数量有关。提议者的工作可能会导致宇宙数量有限这一事实的证明。另一方面，提案人将参与将促进国家教育水平的综合研究和教育活动。

Proposal DMS-0347033Title: CAREER-On the geometry of Kaehler-Einstein manifoldsP.I.: Zhiqin Lu (University of California, Irvine)ABSTRACTThe proposer will study the Szego kernel of certain unitcircle bundle. The study of this is closely related to thestability of manifold. It is now believed that thestability of manifold is the key concept in solving theKaehler-Einstein equation on Fano manifolds. The otherproblem the proposer will work on concerns the geometry ofCalabi-Yau moduli. In particular, the BCOV torsion on theCalabi-Yau moduli may play a key role in verifying somepredictions in Mirror Symmetry. The proposer willparticipate in various programs in education as well asvarious activities to improve the efficiency of education.The proposer is working on some key problems in geometrywhich are not only important to mathematics, but alsoimportant to other sciences like physics. For example,general relativity is the the geometric theory of gravity.One of the application of the proposer's work is related tothe number of "allowable" Universes. The proposer's work maylead to the proof of the fact that the number of theUniverses is finite. On the other hand, The proposer willparticipate the integrated research and education activitiesthat will promote the education level of the nation.