4 problems

In the setting of shifted packets $P_D^{\mathrm{shifted}}$ on $X_1\times\cdots\times X_r$, assume individual equidistribution, or assume $k_1=\dots=k_r=1$. For every pair $i\ne j$…

Let a Gaussian system and a rank-one automorphism be measure-preserving dynamical systems, and call two systems disjoint when their only joining is the product joining. Thouvenot's…

Let $G \curvearrowright (X,\mu)$ and $G \curvearrowright (Y,\nu)$ be free probability-measure-preserving actions, and let $\mu\times\nu$ be their direct-product joining. Direct-pro…

Thouvenot's conjecture. All bounded mildly mixing constructions have minimal self-joinings.