5 problems

Let $d49c$ be the measure obtained in the theorem on unique ergodicity, and consider Bruin–Troubetzkoy interval translation maps of infinite type. Weak-mixing conjecture. Almost al…

Polygonal-billiard conjecture. For almost all simply connected polygonal tables, the billiard flow is ergodic and weakly mixing.

Directional weak-mixing conjecture. For every translation surface that does not factor over the circle, the directionally typical translation flow is weakly mixing.

Let $p(q)$ denote the word complexity of a subshift, namely the number of distinct words of length $q$, and suppose the subshift admits a weakly mixing probability measure. The qua…

Let $(X,\mathscr{B},\mu,T)$ be a measure-preserving system, let $U$ denote its Koopman operator, and let $f\in L^2(X,\mu)$ satisfy … for every $g\in L^2(X,\mu)$. A sequence…