Gromov–Zimmer's quasi-affine rigidity conjecture

Let $D$ be a semisimple Lie group all of whose factors have property $(T)$, or a lattice in such a Lie group. A rigid geometric structure is a geometric structure of the rigid type considered in the source. Gromov–Zimmer's conjecture. Any $D$ action on a compact manifold preserving a rigid geometric structure and a volume form should be generalized quasi-affine. This is a major open problem generalizing the affine-action classification conjecture.