4 problems

Let $G$ be a second countable locally compact group and let $\partial_F G$ be its Furstenberg boundary. For $z\in\partial_F G$, assume that $z$ is a continuity point of the stabili…

Let $G$ be an arbitrary locally compact group, and let $cmu$ be a spread-out probability measure defining a random walk on $G$. Bader–Muchnik conjecture. The Koopman representation…

Let $\Gamma$ be the group, let $\partial\Gamma$ be its boundary, and let $\pi:\Gamma\to\mathcal{U}(\mathcal{H})$ be an irreducible unitary representation weakly contained in the re…

Three-way boundary-realization conjecture. Every tempered representation of a free group satisfies exactly one of these three possibilities: monotony, oddity, or duplicity.