5 problems

Signed-tiling conjecture. If $n=3$ or $n=6$, then the contribution of $L$ is $0$ unless there exists a signed tiling of $L$ by stones, bones, and snakes; if such a signed tiling ex…

Hexagonal-lattice random-current conjecture. All phase transitions of the random current and random-cluster model on the hexagonal lattice coincide:

Let $r_1,r_2,\ldots$ be the positive real numbers of the form … where $j,k$ are integers. A radial Schwartz function is a function $f:\mathbf{R}^2\to\mathbf{R}$ invariant under rot…

Let $r_1,r_2,\dots$ be the positive real numbers of the form … where $j$ and $k$ are integers. Radial Schwartz functions $f\colon{\mathbb R}^2\to{\mathbb R}$ are considered through…

Universal-cover connective-constant conjecture. There exists $k\in\mathbb N\cup\{0\}$ for which