Problems Related to Conformal and CR Geometry

摘要DMS - 0204480。 PI：C。罗宾格雷厄姆这个项目将研究适形和CR几何。 代数，分析和几何方面将被认为是通过引入度量inhigher维与原来的共形或CR几何。 理解更高维度的空间产生了独立的兴趣问题。 动力来自物理学中的AdS/CFT对应关系。保角几何是研究不被保持角度但不一定保持长度的变换所改变的空间性质。保角映射和保角几何多年来在实际问题中得到了大量的应用，例如飞机机翼的设计。 最近，在物理学中所谓的全息对应中，高维的共形几何成为人们非常感兴趣的对象。 这个项目将研究几何空间的基本性质，部分原因是与物理理论的相互作用。

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