CAREER: On the Geometry of Kahler-Einstein Manifolds

University Of California-Irvine, Irvine CA

Investigators

Abstract

Proposal DMS-0347033 Title: CAREER-On the geometry of Kaehler-Einstein manifolds P.I.: Zhiqin Lu (University of California, Irvine) ABSTRACT The proposer will study the Szego kernel of certain unit circle bundle. The study of this is closely related to the stability of manifold. It is now believed that the stability of manifold is the key concept in solving the Kaehler-Einstein equation on Fano manifolds. The other problem the proposer will work on concerns the geometry of Calabi-Yau moduli. In particular, the BCOV torsion on the Calabi-Yau moduli may play a key role in verifying some predictions in Mirror Symmetry. The proposer will participate in various programs in education as well as various activities to improve the efficiency of education. The proposer is working on some key problems in geometry which are not only important to mathematics, but also important 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 to the number of "allowable" Universes. The proposer's work may lead to the proof of the fact that the number of the Universes is finite. On the other hand, The proposer will participate the integrated research and education activities that will promote the education level of the nation.