Conformal geometry and partial differential equations

共形几何和偏微分方程

• 批准号: 1005295
• 负责人: Jie Qing
• 金额: $ 16.17万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005295&HistoricalAwards=false
• 关键词: Conformal; geometry; partial; differential; equations

Dr. Jie Qing proposes to study various problems in conformal geometry and related partial differential equations. 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 mathematical foundations of the holography principle, particularly the so-called AdS/CFT correspondence. Dr. Jie Qing also proposes to continue his study of several geometric problems arising from the mathematics of general relativity. The intellectual merit of this proposal is that consequences of these investigations will give better understanding of geometric structure of manifolds of low dimensions.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. 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 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.

洁清博士建议研究保形几何和相关偏微分方程中的各种问题。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数学基础的几个方面，特别是所谓的AdS/CFT对应。Jie Qing博士还建议继续研究广义相对论数学中的几个几何问题。这一建议的智力价值是，这些调查的结果将得到更好的理解的几何结构的流形的低dimensions.The拟议的研究是研究全息原理，量子引力理论和一些共形场理论。它已经成为数学家和物理学家可以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。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。