Canonical sections of Hodge bundles on moduli spaces

Abstract

We review recent works in [K. Liu, S. Rao, and X. Yang, Quasi-isometry and deformations of Calabi Yau manifolds, Inventiones mathematicae, 199(2) (2015), 423–453] and [K. Liu and Y. Shen, Moduli spaces as ball quotients I, local theory, preprint] on geometry of sections of Hodge bundles and their applications to moduli spaces.