7 problems

Nešetřil–Ossona de Mendez's strong mass-transport conjecture. Every first-order convergent sequence of graphs from ${\cal C}$ has a modeling limit that satisfies the strong finitar…

Well-balanced-class conjecture. Every well-balanced class in

Extremal uniqueness conjecture. Equality holds in the sharp inequality if and only if $f=h_p$ up to translations, dilations and multiplicative constants.

Let $\mathbf L$ be a modeling. Assume: (i) the theory of $\mathbf L$ has the finite model property; (ii) every interpretation of $\mathbf L$ satisfies the finitary mass transport p…

Strong mass-transport conjecture. One can require a version of the strong mass transport principle. The text explains that the inequality is immediate for first-order definable set…

Let $m_1$ be the mass initially concentrated near the unstable peak, let $\tilde{\sigma}$ denote the parameter determining the rescaled Gaussian asymptotic profile of that peak, an…

Let $\pi^0\in{\cal W}_0$ be a path and let $\rho_t(\pi^0(t))$ denote the mass associated with its position at time $t$. Mass-variation conjecture. The function … has locally unboun…