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In this talk we will discuss how we can combine geodesic counting theorems in hyperbolic manifolds and theorems about controlled quotients of virtually special groups to see that every non-arithmetic lattice in PSL(2,C) is the full (orientation preserving) isometry group of some other lattice, and that every isometry of a finite-volume hyperbolic 3-manifold acts non-trivially on the first homology of some finite-sheeted cover. This is joint work with Ian Agol and Yair Minsky.