Some problems in conformal geometry and General Relativity

共形几何和广义相对论的一些问题

• 批准号: 0700535
• 负责人: Jie Qing
• 金额: $ 15.04万
• 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: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0700535&HistoricalAwards=false
• 关键词: Some; problems; conformal; geometry; General

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.

杰青博士建议研究共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一个较为全面的途径，这是非常令人着迷和有希望的。在这个项目中，Jie Qing博士提议研究全息原理的几个方面，特别是与保形几何相关的所谓AdS/CFT对应关系。这些为在共形几何中找到好的全局共形不变量提供了很好的来源，并且被认为比以往更加全面。本研究旨在研究量子引力理论与某些共形场理论之间的全息原理。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极大地提高我们对自然理论的理解。这项提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分校数学系本科和研究生教育计划的一部分。