16 problems

Let $\kappa\in(0,8)$, and consider a multiple-SLE$_\kappa$ process growing $2N$ curves in the upper half-plane from points $x_1<x_2<\ldots<x_{2N}$, with SLE$_\kappa$ partition func…

Multiple SLEs consist of several interfaces starting from the boundary of a domain, with no other marked points. Let $N\geq 2$, let $M=0$, and let each parameter $\kappa_I$ have th…

Existence and uniqueness conjecture. In each polygon, there exists a unique global $\textnormal{-}\mathrm{SLE}_{}$ for each $$ -valenced link pattern $\in$ and for each $ \in (0,…

Chordal ground-solution completeness conjecture. The chordal ground solutions $\mathcal{J}^{(m,n)}_{\alpha}$ constructed from chordal link patterns are exactly all solutions to the…

Linking-probability conjecture. The linking probabilities for multichordal $\mathrm{CLE}_\kappa$ in Theorem are given by the same formula as in the referenced work on connection pr…

Let $n$ growth points and $m$ screening variables define the null-vector equations and Ward identities for multiple radial SLE, and let $u\in\mathbb{H}$ be the marked interior poin…

Let $\mathrm{CLE}_{\kappa}$ denote the conformal loop ensemble with $\kappa\in(8/3,8)$, and consider critical loop $O(n)$ loops with $n\in(0,2]$ and $N\geq2$ alternating boundary i…

Consider the loop $O(n)$ model with $n\in (0,2]$ and boundary condition $\beta\in\mathrm{LP}_N$. Let $\varsigma^{\delta}$ be the random connectivity in $\mathrm{LP}_N$ induced by t…

Let $(\Omega; x_1, \ldots, x_{2N})$ be a polygon, let $\beta\in\mathrm{LP}_N$ be a link pattern, and consider the critical random-cluster model and interfaces from the preceding co…

Let $(\Omega; x_1, \ldots, x_{2N})$ be a polygon and let $\beta \in \mathrm{LP}_N$ be a link pattern. Suppose that a sequence…

Bauer–Bernard–Kytölä conjecture. To these boundary conditions one can associate an SLE partition function $Z(b^{(1)},\dots,b^{(n)})$, with $b^{(1)},\dots,b^{(n)}\in\mathbb{R}$, suc…

Ising crossing-probability conjecture. The crossing probabilities converge according to

Let $\mathfrak{A}\mathrm{rch}$ be the collection of link patterns, and let $(\mathcal{Z}_\alpha)_{\alpha\in\mathfrak{A}\mathrm{rch}}$ be the collection of solutions to the multiple…

Let $N\geq 1$ and let $\mathfrak{A}\mathrm{rch}_N$ denote the set of link patterns with $N$ links. For each $\alpha\in\mathfrak{A}\mathrm{rch}_N$, let…

Let $\mathcal{S}_N$ be the SLE partition-function solution space, let $\mathcal{B}_N$ be the distinguished family of solutions, and let $\mathcal{R}_N\subset\mathcal{S}_N$ be the s…

Connectivity-weight basis conjecture. The set $\mathscr{B}_N$ is the hypothetical basis of $\mathcal{S}_N$, and each $\Pi_\varsigma$ is the corresponding SLE$_\kappa$ partition fun…