6-25【Dylan Cant】Applications of Floer cohomology to the study of contactomorphisms and Legendrians

In this first talk in a series of two talks, I will briefly review the construction of Floer cohomology for contact-at-infinity Hamiltonian systems and Lagrangians in a convex-at-infinity symplectic manifold W and then discuss its applications to the geometry of the contactomorphisms and Legendrians of the ideal boundary W, including applications to orderability and persistence of translated points and Reeb chords.