4 problems

Peterson–Thom conjecture. There exists a unique maximal amenable von Neumann subalgebra $\mathcal{P}$ of $\mathcal{L}(\mathbb{F}_r)$ such that

A II$_1$ factor is nonamenable if it is not amenable, and $L(\mathbb F_2)$ denotes the group II$_1$ factor of the free group on two generators. von Neumann algebraic von Neumann pr…

Let $r>1$ and let $Q$ be a von Neumann subalgebra of the free group factor $L({\mathbb F}_r)$. Assume that $Q$ is diffuse and nonamenable. Positivity conjecture for 1-bounded entro…

Let $t\in(1,\infty]$ and let $N\subseteq L(\mathbb{F}_{t})$ be a maximal amenable von Neumann subalgebra. Regard the following as $N$-$N$ bimodules, where…