Geometric PDE in Confromal Geometry and Relativity

共形几何和相对论中的几何偏微分方程

• 批准号: 0402294
• 负责人: Jie Qing
• 金额: $ 10.2万
• 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: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0402294&HistoricalAwards=false
• 关键词: Geometric; PDE; Confromal; Geometry; Relativity

Proposal DMS-0402294Principal Investigator: Jie Qing (University of California, Santa Cruz)Title: Geometric PDE in conformal geometry and relativityABSTRACTDr. Jie Qing proposes to study conformally compact Einstein manifolds. Conformally compact Einstein manifolds play crucial roles in theso-called AdS/CFT correspondence, which is a very promising theory that predicts certain connections between quantum gravitational theory andcertain conformal field theory. In mathematics it has been knownthat conformally compact Einstein manifolds provide a powerful approach tothe study of conformal geometry. Recent development in the study of thescattering matrix in providing rather global, natural way to understandthe holography principle in physics seems very fascinating and promising. Dr. Jie Qing is also interested in developing and study theory aboutasymptotically AdS/dS space-times. For a start, one considers staticasymptotically AdS/dS space-times. The theory is not as well-known as thestudy of asymptotically flat space-times. But it is as significant, if notmore, in the classic relativity and quantum gravitation theory.The proposed research is to study the primary object in thetheory of 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. It is a part ofthe efforts to find a unified theory for all fundamental interactionsincluding the strong and weak nuclear interactions, electromagnetism, andgravity. Advancements in this field will greatly improve our understandingof the nature in theory. The proposed research is a very important part ofthe undergraduate and graduate education programs in the department ofmathematics at University of California, Santa Cruz.

提案DMS-0402294主要研究者：Jie Qing（加州大学，圣克鲁斯）题目：共形几何和相对论中的几何偏微分方程。解庆提出研究共形紧爱因斯坦流形。共形紧致Einstein流形在AdS/CFT对应中起着至关重要的作用，AdS/CFT对应是一个非常有前途的理论，它预言了量子引力理论和某些共形场论之间的某些联系。在数学中，共形紧致爱因斯坦流形为共形几何的研究提供了一个强有力的途径. 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种相当全面、自然的方法，这似乎是非常迷人和有前途的。Jie Qing博士还对发展和研究渐近AdS/dS时空理论感兴趣。首先，我们考虑静态渐近AdS/dS时空。这个理论并不像对渐近平坦时空的研究那样广为人知。但它在经典的相对论和量子引力理论中同样重要，甚至更重要，本文的研究主要是研究全息理论中的量子引力理论和一些共形场论之间的联系。它已经成为数学家和物理学家可以互动的领域的一部分。它是为所有基本相互作用（包括强、弱核相互作用、电磁学和引力）寻找统一理论的努力的一部分。这一领域的进展将极大地提高我们对自然界的理论认识。本研究是圣克鲁斯的加州大学数学系本科生和研究生教育计划的一个重要组成部分。