Title: Maximal variation of families of curves
Abstract: In this talk, I will show some examples of families of curves that lie in a smooth projective variety with trivial canonical bundle and that have their complex structures vary maximally possible. This validates in some cases Matsushita's conjecture that the variation of Lagrangian fibrations of hyperkähler manifolds should be either zero or maximal. The results are part of a recent and ongoing collaboration with D. Huybrechts.