10 problems

RBPD limit-shape and arctic-curve conjecture. As $n\to\infty$, the height function converges to a deterministic limit shape consisting of four frozen regions adjacent to the domain…

Whole-range arctic curve conjecture. The arctic curve equation remains valid over the whole range $t\in\mathbb{R}$, rather than only on the SE and SW ranges $t\in[\beta(1),\infty)$…

Let $r>1$ and let $t$ be the parameter in the expansion … where $H(x,y,u,v)$ is the leading-order polynomial and $\theta$ is its leading exponent. Leading-exponent conjecture. For…

Arctic-curve symmetry conjecture. The arctic curve is the same for any $0\leq t\leq 1$ and $1/t$, up to the reflection $y=x$.

For a sequence of bounded lecture hall tableaux with limiting height function $h(x,y)=\lim h_n(x,y)/n$, let $u(x,y)$ be the solution of the Burgers equation introduced for the asso…

Let $K(m_x,m_y)$ be the function describing the interacting arctic curve, let $\boldsymbol{\gamma}$ be the model parameter, and let $m_x,m_y$ be magnetisation variables. For…

Envelope conjecture. This envelope is precisely the outer boundary of a larger frozen domain enclosing the fully frozen triangular region and tangent to this region at its endpoint…

Let $\Lambda$ be a generic domain for the six-vertex model, and consider a south side ending at a corner, with the relevant external portion of the Arctic curve lying above that si…

Let $r(z)$ be the scaled logarithmic derivative of the boundary correlation function $h_N(z)$, namely … For the six-vertex model with domain wall boundary conditions, let $t$ and…

Condensation conjecture. For arbitrary choices of the vertex weights, the arctic curve can be characterized by the condition that almost all roots of the corresponding saddle-point…