6 problems

For $p=0,1$, let the associated metric be the BKM metric, and let $L^{{\rm exp}}$ and $L^{x{\rm log}x}$ denote the Zygmund spaces appearing in the construction under discussion. BK…

WYD scalar-curvature conjecture. There exists $\varepsilon>0$ such that, for every $p\in I$, the scalar curvature of the WYD$(p)$ metric is a Schur-increasing function.

Petz's conjecture. The scalar curvature of the BKM metric is a Schur-increasing function; equivalently,

Let $\theta\mapsto\ket{\Psi(\theta)}$ be a smooth pure two-qubit family, let $\rho_A(\theta)$ be its one-qubit reduction, and let $P(\theta)$ be the Riesz projector onto the active…

The GNS-modified monotone metric conjecture. The expression above provides a solution for the problem of simultaneously generalizing Čencov's and Petz's characterizations, namely,…

Extremality conjecture. The function $k_1^\mathrm{WYD}$ is an extreme point of $\mathcal{K}^+$. The function lies on the boundary of $\mathcal{K}^+$; the conjecture concerns whethe…