2 problems

Double Birkhoff averages conjecture. Every $\mathbb{R}^{m}$-system is good for double Birkhoff averages: for every $f_1,f_2\in L^{\infty}(\mu)$ and every…

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…