The purpose of the talk is to study the Hausdorff dimension of limit sets of certain discrete subgroups $\Gamma$ of ${\mathsf{SL}}_d(\mathbb{R})$ (or ${\mathsf{SL}}_d(\mathbb{C})$) that verify a property that we call Frenet. This is an open property in the space $\textrm{hom}(\Gamma,{\mathsf{SL}}_d)$ that implies some form of conformality of the group action when restricted to its limit set.

This is joint work with B. Pozzetti and A. Wienhard