Non linear residually finite hyperbolic groups

Gromov hyperbolic groups were introduced by Gromov in the 80s as a generalization of the class of fundamental groups of closed negatively curved Riemannian manifolds. A fundamental open question in geometric group theory is whether all hyperbolic groups are residually finite, and if such examples exist, they are necessarily non-linear. In this talk, I will describe a construction of the first known examples of non-linear hyperbolic groups which are residually finite. This is joint work with Nicolas Tholozan.