Problems Related to Conformal and CR Geometry

摘要DMS-0204480。派：C·罗宾·格雷厄姆这个项目将学习共形几何和CR几何。代数、解析和几何方面将通过引入与原始共形或CR几何相关联的更高维度的度量来考虑。对高维空间的理解引发了独立兴趣的问题。物理中的ADS/CFT对应提供了动力。共形几何是研究空间的性质，这些性质不被保持角度但不一定是长度的变换所改变。多年来，保角映射和几何在实际问题中得到了大量的应用，例如飞机机翼的设计。高维的构象几何最近已经成为物理学中所谓的全息对应的许多有趣的对象。这个项目将研究基本几何空间的性质，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.