Resumen de Lagrangian submanifolds: from the local model to the cluster complex

François Lalonde

• In these notes, I will present collaborative works on Lagrangian submanifolds that I realised mainly with Octav Cornea (the cluster complex, which naturally leads to a universal Lagrangian Floer theory), but also, at an earlier stage, with Jean-Claude Sikorav. To cover the subject in a more complete and adequate way, I will also mention very recent works by Barraud� Cornea and byWelschinger, closely related to the subject of these notes. The aim of the cluster machinery is to resolve the well known problem of real codimension 1 bubbling off of disks in the Gromov�Floer theory; see Fukaya�Oh�Ohta�Ono (especially the two lectures by Oh and Ono in these proceedings) for a different, earlier, approach.