# Geometry and Topology: Non-displaceable Lagrangian links in four-manifolds

• Date: –15:00
• Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
• Lecturer: Cheuk Yu Mak (University of Cambridge)
• Organiser: Matematiska institutionen
• Contact person: Maksim Maydanskiy

Abstract: One of the earliest fundamental applications of Lagrangian Floer theory is detecting the non-displaceablity of a Lagrangian submanifold. Many progress and generalisations have been made since then but little is known when the Lagrangian submanifold is disconnected. In this talk, we describe a new idea to address this problem. Subsequently, we explain how to use Fukaya-Oh-Ohta-Ono and Cho-Poddar theory to show that for every S^2 \times S^2 with a non-monotone product symplectic form, there is a continuum of disconnected, non-displaceable Lagrangian submanifolds such that each connected component is displaceable. This is a joint work with Ivan Smith.