Mathematical Sciences: Hodge Theory

点击翻译按钮获取中文摘要

Professors Kaplan and Cattani will investigate several questions concerning the properties of flat holomorphic bundles carrying additional structures such as polarized variation of Hodge structure or a Higgs field. They plan to study the local monodromy of such bundles with applications to the fine structure of modular varieties, the characterization of maximal variations of Hodge structure, and the construction of harmonic metrics. This research lies at the interface of algebraic and differential geometry. The objects under study are algebraic varieties, essentially the zero sets of polynomials, but the methods used to study these objects are analytic. This mix of algebraic and differential geometry has been particularly successful in attacking problems which did not yield to purely algebraic methods.