Problems Related to Conformal and CR Geometry

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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.