Complex hyperbolic deformations of cusped hyperbolic lattices

After reviewing some classical results about rigidity and
flexibility of lattices in semisimple Lie groups and known results in
dimension 2, we will discuss the existence and potential
discreteness/faithfulness of deformations of cusped lattices of SO(3,1)
into SU(3,1). We will focus on the cases of small Bianchi groups (joint
with M. Thistlethwaite) and the figure-eight knot group (joint with S.
Ballas and P. Will), as well as the general behavior of bending
deformations in all dimensions.