3 problems

Katok–Spatzier conjecture. Up to finite cover, the action is $C^\infty$ conjugate to an algebraic action.

Classification conjecture. Every irreducible higher-rank ${\mathbb Z}^k$- or ${\mathbb R}^k$-Anosov action on any compact manifold is smoothly conjugate to an algebraic action.

Infranilmanifold global rigidity conjecture. All irreducible Anosov genuine $\mathbb{Z}^r$-actions on compact infranilmanifolds should be $C^\infty$-conjugate to actions by affine…