10 problems

Positivity conjecture. For bipartite lattices, the coefficients satisfy $C_k\geq 1$.

According to the source, a two-column configuration is admissible when its occupation values $\{\varepsilon_j,\mu_j\}$ satisfy … For the CDP model, Pearce–Rasmussen selection rules…

Let $G$ be a minimal bipartite graph on a torus whose Newton polygon has $d+2$ vertices, and let $\mathcal F \colon \mathcal B \to \mathcal S$ be the map from the space of white da…

The dimer model is a probability measure on perfect matchings of a finite weighted graph; for planar bipartite graphs, its centered height function $h-{E}(h)$ describes the macrosc…

Let $\Omega_\xi$ be the polygonal domain associated with the scaling limit of the origami maps constructed from perfect t-embeddings, and let gaseous bubbles denote regions of the…

Let $\bar{\mathcal G}$ be the shifted reflected graph described in the source, and fold a dimer configuration onto itself through reflection across the real line, erasing the verti…

Let $\hat{\mathcal G}$ be obtained by adjoining to a graph $\mathcal G$ its reflection across the real axis while retaining one copy of vertices on the real axis. Let $M$ be an inf…

For any $z>0$, superimpose two independent free boundary dimer models in the upper half-plane, and consider the resulting collection of boundary-touching curves. Free-boundary dime…

Consider two independent dimer configurations and superpose them, obtaining loops that are level lines of the difference of their dimer height functions. Kenyon's conjecture. The l…

Let $G$ be a general $\mathbb{Z}^2$-periodic graph, and consider the spanning-forest measure with slope parameter. A configuration has zero slope when its slope is $0$. Zero-slope…