3 problems

Joint ergodicity conjecture. The polynomials $p_1,\ldots,p_\ell$ are jointly ergodic for $(X,\mathcal{X},\mu,U)$ if and only if: (1) the product action…

Let $(X,\mathcal{X},\mu,T_1,T_2)$ be a measure-preserving system. Joint ergodicity for logarithmic averages means convergence of the corresponding logarithmically weighted multiple…

Let $(X,\mathcal X,\mu)$ be a probability space, let $T_1,\ldots,T_\ell$ be commuting measure-preserving transformations, and let $p_1,\ldots,p_\ell\in\mathbb Z[n]$. A sequence of…