Abstract: (Sorry for the last-minute email. No worries if you cannot make it!) We will present a geometric model of the Auslander--Reiten quiver of a type A quiver together with a stability function for which all indecomposable modules are stable. We also introduce a new Catalan object which we call a maximal almost rigid representation. We define a partial order on the set of maximal almost rigid representations and use our new geometric model to show that this partial order is a Cambrian lattice. If there is time, we will discuss a connection to the biCambrian lattice of diagonal rectangulations (which are counted by the Baxter numbers). This is based on joint work with E. Barnard, E. Meehan, and R. Schiffler.