9 problems

Dimension bound conjecture. The dimension of $M$ must be at least $n$.

Fisher–Melnick classification conjecture. For every smooth action $\rho:\Gamma\rightarrow\operatorname{Diff}(M)$, one of the following holds:

Let $n$ be an integer, let $\Gamma$ be a lattice in $\mathrm{SL}(n,\mathbb{R})$, and let $\Gamma$ act by volume-preserving diffeomorphisms on an $n$-dimensional manifold. Blow-up c…

Let $n\geq 3$, let $\Gamma<\operatorname{SL}(n,{\bf R})$ be a lattice, and let $M$ be a compact manifold of dimension $n$. A volume-preserving blow-up or two-sided blow-up is one i…

Let $n\geq 3$, let $\Gamma<\operatorname{SL}(n,{\bf R})$ be a lattice, and let $M$ be a compact manifold of dimension $n$. An action built from tori, $G$-tubes, $G$-disks, blow-ups…

Let $G$ be a higher-rank simple Lie group, let $\Gamma<G$ be a lattice, let $M$ be a compact manifold, and let $\rho:\Gamma\to\operatorname{Diff}(M)$ be an action. Assume that the…

Let $G$ be the ambient group, let $\Gamma<\operatorname{SL}(n,\mathbb{R})$ be a lattice acting on an $n$-manifold $M$, and let $P$ be the subgroup appearing in the induced action o…

Let $n$ be an integer, let $\Gamma<\operatorname{SL}(n,\mathbb{R})$ be a lattice, and let $M$ be an $n$-manifold on which $\Gamma$ acts stiffly. Stiff actions conjecture. Either th…

Let $G$ be a real semisimple algebraic group with no compact factors and let $\Gamma$ be an irreducible lattice in $G$. Suppose that … and that every semisimple subgroup…