CAREER: On the Geometry of Kahler-Einstein Manifolds

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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.