Some problems in conformal geometry and General Relativity

清杰博士提出要研究保形几何中的各种问题。散射矩阵研究的最新进展为理解物理学中的全息原理提供了相当全面的方法，这似乎是非常迷人和有前途的。Jie Qing博士建议在这个项目中研究全息原理的几个方面，特别是所谓的AdS/CFT对应，与共形几何有关。这为在共形几何中寻找良好的整体共形不变量提供了重要的资源，并且被认为比以往任何时候都更全面。本研究的目的是研究与量子引力理论和一些共形场论相关的全息原理。它已经成为数学家和物理学家可以很好地互动的领域的一部分。这一提议的一个更广泛的影响是，这一研究领域的进步将大大提高我们对自然的理论理解。这项建议的另一个更广泛的影响是教育。拟议的研究项目将研究活动作为加州大学圣克鲁斯数学系本科和研究生教育课程的一部分。

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.