## On Zimmer's conjecture

The group $\mathrm{SL}_n(\mathbb Z)$ (when $n > 2$) is very rigid, for example, Margulis proved all its linear representations come from representations of $\mathrm{SL}_n(\mathbb R)$ and are as simple as one can imagine. Zimmer's conjecture states that certain "non-linear" representations ( group actions by diffeomorphisms on a closed manifold) come also from simple algebraic constructions.