Jason Manning Title: Residual finiteness and separability of quasi-convex subgroups Abstract: We show that if all hyperbolic groups are residually finite, then all quasi-convex subgroups of hyperbolic groups are separable. One way to think of this result is as a tool in the search for an example of a non-residually finite hyperbolic group. The main tool is relatively hyperbolic "Dehn filling", applied to a peripheral structure induced by a quasi-convex subgroup. We show that, after filling, the quasi-convexity of the original subgroup persists, and that a certain measure of its complexity (the "width") decreases. This is joint work with Ian Agol and Daniel Groves. (These results have been extended to a class of relatively hyperbolic groups in joint work with Eduardo Mart\'inez-Pedroza -- see Mart\'inez-Pedroza's talk at this conference for more.)