**"Boomerang subgroups and the Stuck-Zimmer theorem"**
#### Lederle, WaltraudWe introduce the notion of boomerang subgroups of a discrete group. Those are subgroups satisfying a strong recurrence property, when we consider them as elements of the space of all subgroups with the conjugation action. We prove that every boomerang subgroup of $\mathrm{SL}_n(\mathbb{Z})$ for $n \geq 3$ is finite or of finite index. Thus we give a new proof of the Stuck-Zimmer rigidity theorem for $\mathrm{SL}_n(\mathbb{Z})$ avoiding almost all measure theory.
This is joint work with Yair Glasner. |