37 problems

Consider the $|\varphi|^4$ model with free boundary conditions (FBC), and let $\chi_{g,\nu,N}^{\rm F}$ denote its susceptibility, while $\chi_{g,\nu,N}$ denotes the susceptibility…

A conformal field theory is deformed by relevant bulk operators, and its ground state is considered in relation to conformal boundary states. Cardy's conjecture. The ground state o…

Let $k\geq 2$, $J<0$, and $\beta>\beta^1_{\rm cr}$. Let $\mu^*_+$ be the top symmetric translation-invariant splitting Gibbs measure, and let $\omega^{(n)}$ denote the boundary con…

Let $\mathcal{M}$ be a manifold with boundary $\partial\mathcal{M}$, and let $B_m$ denote the supergravity field appearing in the boundary action. The action may contain terms prop…

Consider the coupled system $\overline{\mathcal{T}}_{\text{min}}\times T_{\mathfrak g}$, where $\overline{\mathcal{T}}_{\text{min}}$ is the orientation reversal of the minimal SCFT…

Geometric-frustration conjecture. For Neumann boundary conditions, the effects of geometric frustration would be lost in the $\mathbf{M}$ profiles, and the $\mathbf{M}$ profiles wo…

An RCFT has vanishing gravitational anomaly when its left- and right-moving gravitational anomaly cancels. A boundary condition has finite $g$-function when its boundary entropy pa…

Consider the $\mathcal{N}=1$ Maruyoshi–Song Lagrangian reduced on the cigar, and the boundary chiral and Fermi multiplets introduced to reproduce the vacuum and non-vacuum characte…

Let $\mathrm{SM}(3,5)$ denote the fermionic minimal model and let $\mathrm{SO}(1)_1$ denote the invertible spin-TQFT factor. Consider the bulk TQFT associated with the fourth-sheet…

The Navier–Stokes–Cahn–Hilliard equations describe diffuse-interface two-phase flow, with interface thickness $\varepsilon$, mobility $m$, and viscosity $\eta$. The diffusive slip…

Let $M$ be the matrix resulting from the compatibility boundary condition equations on a Cartesian grid with Dirichlet or Neumann boundary conditions, or at a corner where Dirichle…

Consider Bernoulli bond or site percolation in dimension $d>6$ on the box $\Lambda_r$, using only bonds or sites in the box for free boundary conditions. Let $p_c$ be the infinite-…

Free-boundary effective critical point conjecture. There exists such a $\beta_{c,r}$ for which all statements of the non-Gaussian limit and universal profile conjecture hold with…

A generalized Wentzell condition models transmission through a highly conductive layer, and numerical experiments suggest that such a layer may be fractal, meaning that its geometr…

Let $a9$ be a region, and let $S_\mathrm{E}^{\partial \Omega}$ be a boundary action associated with the boundary $\partial \Omega$ as in the Euclidean action with boundary conditio…

The paper considers a compressible magnetohydrodynamic system with magnetic field ${\bf B}$ in a domain coupled to an exterior region, where the interface conditions include contin…

Let $\Omega$ be an arbitrary Lipschitz domain, let $\{v_k\}_{k\in\mathbb N}$ be the orthonormal eigenfunction system on $\partial\Omega$ described above, and let … where the indepe…

In a three-dimensional $\mathcal{N}=4$ gauge theory, let exceptional Dirichlet boundary conditions be boundary conditions with the exceptional properties considered in the source,…

Consider linear dispersive evolution equations on an interval with boundary conditions that do not couple the interval endpoints. In the Robin Schrödinger case, the solution at rat…

Let $T>0$, let $m$ be the porous-medium exponent, and let $g:{\mathbb T}\to[0,1]$ be measurable. For each $\kappa>0$, let…

Let two 3d dualities relate gauge theories defined on half spaces $\mathbb{R}_{\le 0} \times \mathbb{R}^2$ or on $S^1 \times D^2$. Consider the Neumann and Dirichlet boundary condi…

New-boundary-condition conjecture. This extra boundary condition may correspond, in the scaling limit, to the New boundary condition discovered for the fixed-lattice Potts model.

Gravitational analogue conjecture. The newly derived boundary condition corresponds to the gravitational analogue of the new' boundary condition for the 3-state Potts model.

For a smooth shape, consider eigenfields of the vector Laplacians represented as $1$-forms or $2$-forms, with either normal or tangential boundary conditions. The associated gradie…

Complete Lagrangian boundary-condition conjecture. The boundary condition