2 problems

Let $G$ be a group acting by isometries on a median space $X$. Proposition FHFM states that if $G$ is a Kazhdan group, then every action of $G$ on a median space is bounded, while…

Nica's conjecture. For discrete countable groups, the converse implication in the first assertion and the direct implication in the second assertion hold: if every continuous isome…