Problems Related to Conformal and CR Geometry

University Of Washington, Seattle WA

Investigators

Abstract

ABSTRACT DMS - 0204480. PI: C. Robin Graham This project will study conformal and CR geometry. Algebraic, analytic, and geometric aspects will be considered via the introduction of metrics in higher dimensions which are associated to the original conformal or CR geometry. Understanding the higher dimensional spaces gives rise to problems of independent interest. Motivation is provided by the AdS/CFT correspondence in physics. Conformal geometry is the study of properties of space which are unchanged by transformations which preserve angles but not necessarily lengths. Conformal mapping and geometry has found numerous applications to practical problems for many years, such as the design of airplane wings. Conformal geometry in higher dimensions has recently been the object of much interest in so-called holographic correspondences in physics. This project will study properties of the underlying geometric spaces, partially motivated by the interaction with the physical theories.