5 problems

Let $D$ be a simply connected domain, let $a,b\in\partial D$ be distinct boundary points, and consider the chordal $\textrm{SLE}_\kappa$ trace from $a$ to $b$, modulo reparameteriz…

Let $\mathbb{U}$ be the unit disk and consider a square grid of mesh $\epsilon$. Let the uniform measure be taken on simple grid paths from $0$ to $\partial\mathbb{U}$, and separat…

Let $\gamma$ be the trace of chordal $\textrm{SLE}_\kappa$ in the upper half-plane. SLE8 trace continuity conjecture. For $\kappa=8$, the trace $\gamma$ is almost surely a continuo…

For $\kappa\in[0,8]$, let $\mathrm{SLE}_\kappa$ denote Schramm–Loewner evolution with parameter $\kappa$, and let its trace be the associated random curve. SLE trace minimality con…

Let ${\mathbb P}_{LC^0}$ be the limiting loop measure associated with the zero-curvature scaling, and let $\Omega_1$ denote the event that the loop has nonzero area. Macroscopic-lo…