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Explore complex geometry and Hodge theory in this 59-minute lecture by Kang Zuo from Johannes Gutenberg Universität Mainz. Delve into the study of complex quasi-projective manifolds and their smooth compactifications, focusing on the geometry of log spaces in relation to families of projective manifolds. Examine two types of graded Higgs bundles: the system of Hodge bundles arising from variation of Hodge structures, and the deformation Higgs bundle extending the Kodaira-Spencer map. Learn about the construction of a non-trivial Higgs map connecting these bundles, and discover how Griffiths' curvature formula can be applied to obtain insights into the structure of log differential forms, generalizing the Griffiths-Schmid theorem on strict negativity of horizontal period mappings.
