2 problems

Let $T$ be a rank-one transformation associated with a sequence $(r_n,s_n)_{n=1}^\infty$, where the classical staircase case is $r_n=n$. Smorodinsky's staircase mixing conjecture.…

Let $T$ be an ergodic transformation, and write $\Cal M(T)$ for its spectral multiplicity set. Let $E=\Cal M(T)$. Mixing realization conjecture. There exists a mixing transformatio…