4 problems

Unitary representability conjecture. For every Tikhonov space $X$, there exists a metric space $M$ of $L^1$-type such that $F(X)$ is isomorphic to a subgroup of the group of isomet…

Polar–hyperpolar conjecture. The classes of polar and hyperpolar actions on compact irreducible symmetric spaces of higher rank coincide.

Scaling nonvanishing conjecture. Given $n$ and $v>0$, there is a positive function $\Phi(\delta,n,v)$ such that every isometry of $M$ is scaling $\Phi(\delta,n,v)$-nonvanishing at…

Consider the double-coset $G$-spaces of the form $K\backslash L/\Gamma$, where $L$ is a semisimple Lie group with an irreducible lattice $\Gamma$ and a compact subgroup $K$, and th…