Benjamin Bakker, Hodge Theory and Lagrangian Fibrations

Compact hyperkahler manifolds X are higher-dimensional generalizations of K3 surfaces; their geometry is tightly constrained by the existence of a holomorphic symplectic form. For example, a result of Matsushita says the only nontrivial fibration structures f:X→B they admit are fibrations by Lagrangian tori. In this talk, I will give an overview of how Hodge theory connects the geometry of B to the variation of these tori in moduli, and how Hodge-theoretic techniques can be used to understand B both locally and globally.