Stabilizers of $\mathbf R$-trees with free isometric actions of $F_n$

We prove that if T is an $\mathbf R$-tree equipped with a minimal free isometric action of $F_N$ then the $Out(F_N)$-stabilizer of the projective class [T] of [T] is virtually cyclic. As an application, we obtain a new proof of the Tits Alternative for "dynamically large" subgroups of $Out(F_N)$. The talk is based on joint work with Martin Lustig.