Geometric PDE in Confromal Geometry and Relativity

University Of California-Santa Cruz, Santa Cruz CA

Investigators

Abstract

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