Some problems in conformal geometry and General Relativity

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Dr. Jie Qing proposes to study various problems in conformal geometry. Recent development in the study of the scattering matrix in providing rather global way to understand the holography principle in physics seems very fascinating and promising. Dr. Jie Qing proposes in this project to investigate several aspects of the holography principle, particularly the so-called AdS/CFT correspondence, related to conformal geometry. These provide great sources to find good global conformal invariants in conformal geometry and is believed to be rather comprehensive than ever.The proposed research is to study the holography principles that relate quantum gravitation theory and some conformal field theory. It has become a part the field where mathematicians and physicists can interact very well. One broader impact of this proposal is that advancements in this field of research will greatly improve our understanding of the nature in theory. The other broader impact of this proposal is to the education. The proposed research project incorporates research activities as a part of the undergraduate and graduate education programs in the department of mathematics at UC Santa Cruz.