3 problems

Let $G$ be an icc property (T) group with $\operatorname{Out}(G)=\{e\}$ and no characters. Popa's strengthening of Connes' rigidity conjecture. The group von Neumann algebra satisf…

Let $G_1,\dots,G_n$ be connected non-compact simple real Lie groups with finite center, and let $\Gamma$ be an icc irreducible lattice in $G_1\times\dots\times G_n$. Ioana's primen…

Let $G=PSL(n,\mathbb Z)$ with $n\geq 3$, let $L(G)$ denote its group von Neumann algebra, and let $L(G)^t$ denote its amplification by $t>0$. A group factor is a von Neumann algebr…