5 problems

Let $G_0$ be a real linear simple Lie group of real rank at least $2$, let $K$ be a maximal compact subgroup of $G_0$, and let $\Gamma$ be a discrete subgroup of $G_0\times G_0$ ac…

Let $\Gamma$ be the arithmetic group specified by the local-to-global conjecture above. A group $G$ is flexibly stable if every sufficiently accurate approximate homomorphism from…

Let $\Gamma$ be a noncocompact irreducible arithmetic group, and let $\operatorname{rank}_{\mathbb{R}}\Gamma$ denote its real rank. A group is boundedly generated by unipotent subg…

Let $\Gamma$ be a noncocompact arithmetic subgroup of either $\operatorname{SL}(3,\mathbb{R})$ or $\operatorname{SL}(3,\mathbb{C})$. A faithful action on $\mathbb{R}$ means an acti…

Let $\Gamma$ be a non-cocompact lattice in either $\mathop{\mathrm{SL}}\nolimits(3,\mathbb{R})$ or $\mathop{\mathrm{SL}}\nolimits(3,\mathbb{C})$. Non-cocompact rank-three conjectur…