Appears in collection : Mohamed Abouzaid - Lagrangian Floer cohomology in families

We will begin with a brief overview of Lagrangian Floer cohomology, in a setting designed to minimise technical difficulties (i.e. no bubbling). Then we will ponder the question of what happens to Floer theory when we vary Lagrangians in families, which we will not require to be Hamiltonian. We will see rigid analytic spaces naturally arise from such families; these spaces are the analogue of complex analytic manifolds over the Novikov field. In order to be faithful to the theme of the conference, we will end by constructing lots of moduli spaces in order to see that Floer complexes give rise to analytic coherent sheaves. In preparation, for the course, reading arXiv:1404.2659 is recommended http://arxiv.org/pdf/1404.2659.pdf , while reading arXiv:1408.6794 is definitely not recommended. A revised version of the second reference is in preparation, and should be available by the beginning of the summer school.