New challenges in contact and symplectic topology – COSY

This project will combine the expertise of many specialists in contact and symplectic topology. Our research objectives will concentrate around two specific themes: Lefschetz fibrations and open book decompositions on the one hand and persistent homology on the other hand. Lefschetz fibrations and open book decompositions are central tools to understand the structure of symplectic and contact manifolds. We plan to use these notions in order to derive new constraints on the topology of Lagrangian submanifolds. We also plan to gain a better understanding of their holomorphic curves invariants and of their properties, using the very recent theory of convex hypersurfaces. Exciting new results in C^0 symplectic topology were obtained using persistent homology. We plan to use it in order to extract richer information from homological invariants constructed using holomorphic curves, generating families or sheaves.