7 problems

Regular-polygon t-immersion conjecture. All $\beta(C)={n-2\choose k-1}$ solutions give rise to t-immersions, which are automatically t-embeddings.

Let a limiting t-surface be described by the parametrization in the source, with cusp apexes $P_i$ and parameters $a$ and $t$. The boundary points determine the parameter $a$. Cusp…

Consider a dimer model exhibiting gaseous phases, with an associated t-surface and origami map. A maximal surface is a space-like maximal surface in the ambient Minkowski space. Ga…

Let a dimer model have a scaling limit whose t-surface has cusp locations, and let the model's global fluctuations contain a discrete Gaussian component with a shift. Cusp-location…

Perfect t-embedding conjecture. Every sufficiently nondegenerate weighted bipartite graph $(\Gamma,\operatorname{wt})$ of type $(k,2k)$ admits a perfect t-embedding, and this perfe…

Existence and uniqueness conjecture. Perfect t-embeddings of nice planar bipartite graphs should exist in general, and should be unique up to the natural group of symmetries.

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…