Properly proximal groups and their von Neumann algebras

We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact non-elementary convergence and lattices in non-compact semi-simple Lie but excludes inner amenable groups. show that crossed product II$_1$ factors arising from free ergodic probability measure preserving actions groups this have at most one weakly compact Cartan subalgebra, up to unitary conjugacy. As an application, we obtain the first $W^*$-strong rigidity results for $SL_d(\mathbb Z)$ $d \geq 3$.