7 problems

Let graphons be measurable symmetric functions representing limits of dense graphs, and let subgraph density constraints prescribe the densities of specified finite graphs. A stoch…

Barvinok's marginal-distribution conjecture. The limiting marginal distribution of an entry is Bernoulli when $b=1$ and geometric when $b=\infty$, with mean given by the correspond…

Erdős–Gallai–tameness conjecture. The quadratic-gap Erdős–Gallai condition is equivalent to $\delta$-tameness in the sense of Barvinok and Hartigan.

Polynomial-complexity conjecture. A sufficient condition to compute $W^{*(r,d)}(\mathcal{F},u)$ in polynomial time is that $W^{*(r,d)}(\mathcal{F},u)$ has only one global/local min…

Let $X_1,\ldots,X_n$ be independent random variables taking values in $\{0,1,\ldots,r\}$, and let … For $X_1,\ldots,X_{n-1}$, consider the uniform distribution on $\{0,r\}$. For…

Let $B$ be a Euclidean ball, and let $u$ be a maximising probability measure for the maximum diversity of $B$. Euclidean-ball support conjecture. The support of $u$ is a fini…

Pairwise maximum-entropy conjecture. The inequality holds when using the pairwise maximum entropy solution $\hat{P}$, with no higher-order interactions.