abstract: The first talk (http:/www.ma.ic.ac.uk~smscrmCastanoBernard.html) explains that one could use affine manifolds with singularities and local models of singular fibres to construct Lagrangian fibrations of Calabi-Yau manifolds. In this talk I will explain some joint work with R. Castano-Bernard where we propose a construction of a model of the so-called negative fibration. It is a piece-wise smooth Lagrangian fibration which fails to be smooth only over the singular fibres. We expect to be able to glue this model to Lagrangian torus fibrations coming from singular affine manifolds with singularities.