Talk abstract: Stokes flows in confined geometries have recently attracted much attention due to their relevance to both lab-on-a-chip design as well as low Reynolds number locomotion. Most two-dimensional problems have studied flows in simple geometries, such as a half plane. We present a new method of finding exact solutions for Stokes flows in more complicated domains. We also present a new way of modelling micro-swimmers and show how they interact with walls, as well as walls with gaps. This results in interesting dynamical systems which exhibit rare gluing bifurcations as well as hydrodynamical bound states, which are useful for mixing problems in Stokes flows.