Mathematical Sciences: Gaussian Maps and Topology of SurfaceSingularities

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This research is in algebraic geometry, specifically studying invariants and deformations of surface singularities. The principal investigator will study two problems in the topology of links of surface singularities; one involves Casson's invariant of a homology 3-sphere, the other involves a mysterious new invariant arising from the principal investigator's work on Miyaoka's inequality for projective surfaces. He will also study a problem arising from surface singularities, the study of "Gaussian maps" for curves and homogeneous spaces. The subject of this research is the topology of algebraic surfaces and their singularities. Certain numerical invariants are attached to these objects which help in classifying them. The principal investigator will study these invariants.