Geometry of rationally connected varieties

We recall that a complex quasi-projective variety is said to be rationally connected if two general points of the variety can be connected by a rational curve. The class of rationally connected varieties forms a building block in birational geometry. For example, mildly singular Fano varieties are rationally connected. In this lecture, I will present some results and problems in two different topics in rationally connected varieties: "Tensor differential forms on rationally connected varieties" and "Bases of Lagrangian fibrations".