4 problems

Let $G$ be a countable discrete group with a left-invariant partial order $\preceq$. Let $f\in \mathbb{Z}(G)$ be semi-lopsided and satisfy … Set $m=\tau(f)$. Suppose either that…

Centralizer conjecture. If the centralizer of $T$ is ergodic, then the sofic entropy and quenched sofic entropy coincide; if it is weakly mixing, then the sofic entropy and doubly…

Let $r\in\mathbb N$, and let $A$, $B$, and $C$ be $Z(F_r)$-modules in an exact sequence … Suppose that the actions of $F_r$ on $(\widehat{A},\lambda_{\widehat{A}})$,…

Failure of additivity conjecture. There is such an exact sequence for which