Mathematical Sciences: "Topics in Differential and Complex Geometry"

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9504908 Poon The proposed research deals with smooth 4-manifolds and complex algebraic surfaces. The investigator will use twistor theory to tackle various problems in smooth 4-manifold theory; algebraic surfaces of general type are to be considered as well. This latter project is a continuation of the Kadaira-Enriques program, where they give a coarse classification of (algebraic) complex surfaces. Smooth four-manifolds are generally considered to be the most difficult and interesting class of manifolds. For example, it is known that only in dimension 4 there exists an 'exotic' smooth structure. These manifolds also pertain to various models of the universe according to general relativity theory.