Speaker: Christian Schnell

Title: Hodge theory and Lagrangian fibrations

Abstract: This is a talk about Lagrangian fibrations on holomorphic symplectic manifolds, for example the Hitchin fibration (on the moduli space of Higgs bundles over a curve). The general fiber of such a Lagrangian fibration is an abelian variety, but the singular fibers are rather mysterious. There were several beautiful conjectures about the Hodge theory of Lagrangian fibrations, proposed by Junliang Shen, Qizheng Yin, and Davesh Maulik. I will try to introduce the conjectures and give an idea of the proof