Title: Compactification of Lagrangian fibrations
Abstract: Lagrangian fibered Hyper-Kähler manifolds are the natural generalization of elliptic K3 surfaces and have been used to study and construct examples of compact Hyper-Kähler manifolds and (possibly singular) symplectic varieties. In this talk I will talk about some recent compactification techniques I introduced for quasi-projective Lagrangian fibrations, with applications to the study of Prym, Intermediate Jacobian, and Albanese fibrations.