Mathematical Sciences: Geometry of Period Mappings and Abelian Varieties

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This research will be in algebraic geometry, especially the study of geometrically defined subvarieties of moduli spaces of curves, hypersurfaces, and abelian varieties, and of more general period spaces, and applications to period maps. In particular they plan to extend their analysis of the geometry of discriminant loci for families of hypersurfaces to mappings and families of algebraic cycles. One principal application will be to the study of the Hodge problem for one cycles on projective threefolds and two-cycles on abelian varieties.