Pseudoholomorphic curves (pioneered by Gromov in ’85) have become a staple of the study of low dimensional TQFT’s over the past decades. Before one encounters Symplectic Field Theory, for which the analysis of spaces of such maps is a central object, we pause along the way to investigate some interactions in low dimensions; we look at 4 dimensional symplectic cobordisms with contact type boundaries, where we will state a result that extracts unknotted orbits of the contact dynamics (on the boundary) out of a purely topological setting (on the symplectic 4-manifold). Conversely we will see how dynamical constraints on the contact manifold sometimes suffice to classify the 4 -manifold up to diffeomorphism or even symplectomorphism.
Details about the programme of seminars organised by SMSAS postgraduate research students for SMSAS postgraduate research students.