Title: Isotrivial Lagrangian fibrations for hyper-Kähler manifolds

Abstract: Hyper-Kähler manifolds are fundamental building blocks in the classification of algebraic varieties, occupying a central position in complex geometry. While they are among the most promising candidates for a complete classification, many fundamental questions remain open. A key approach to understanding their structure is through Lagrangian fibrations—fibrations by abelian varieties of half the dimension. These fibrations naturally fall into two categories: those with maximal variation and those that are isotrivial. In this talk, I will discuss the classification of isotrivial Lagrangian fibrations and present recent developments in the field. This is based on joint work with Yoon-Joo Kim and Olivier Martin.