Hodge Theory, Higgs Bundles on Moduli Spaces of Manifolds and Hyperbolicity I

Explore the intricate connections between Hodge theory, Higgs bundles, and moduli spaces of manifolds in this advanced mathematics lecture. Delve into the geometry of log spaces and variation of Hodge structures as they relate to families of projective manifolds. Examine two types of graded Higgs bundles: systems of Hodge bundles arising from variation of Hodge structures and deformation Higgs bundles extending the Kodaira-Spencer map. Investigate the construction of a non-trivial Higgs map connecting these bundles, and discover how Griffiths' curvature formula can be applied to obtain insights into log differential forms. Gain a deeper understanding of complex algebraic geometry and its applications to the study of manifold hyperbolicity.