Appears in collection : Géométrie algébrique en l'honneur de Claire Voisin

For a Lagrangian fibration from a projective irreducible symplectic variety, the perverse numbers of the fibration are equal to the Hodge numbers of the source variety. I will try to explain this fact from two perspectives: its relation with the LLV algebra (under the hyper-Kähler SYZ conjecture), and possible enhancements to the level of sheaves/categories. The second part uses no hyper-Kähler geometry and makes sense for non-proper source varieties. Joint work with Junliang Shen.