5 problems

The Fourier lower-bound conjecture.

Let $\Gamma$ be a group with property $[T_n]$, and let $M$ be a von Neumann algebra on which $\Gamma$ acts by automorphisms preserving a faithful normal state. The invariant-state…

A Banach space $X$ is $\mathrm{K}'$-convex if it is isomorphic to a Banach space $E$ for which there exists an operator-space structure such that the vector-valued Schatten space…

The left-ideal lower-bound conjecture. For the action of $\Gamma$ by left multiplication,

Let $\Gamma$ be an $\mathcal{R}^{\omega}$-embeddable group, fix $2<p<\infty$, and consider the multiplication action of $\Gamma$ on $L^{p}(L(\Gamma),\tau_{\Gamma})^{\oplus n}$. Let…