4 problems

The Schramm–Loewner evolution (SLE) is a family of random non-self-crossing curves indexed by $kappa i(0,infty)$, originally parametrized by half-plane capacity; its natural parame…

Good-parameter conjecture. Every $\kappa<8$ is good. If true, the construction would yield continuity of the natural parametrization process $\Theta_t$ throughout the full range…

SLE natural-parametrization existence conjecture. The asserted existence statement should hold for all $\kappa<8$; the paper proves it for $\kappa<\kappa_0$. Establishing the proce…

For fixed $\kappa\in(0,8)$, let $\gamma$ be an $SLE_\kappa$ curve with Hausdorff dimension $d=1+\kappa/8$. Suppose a locally finite measure on $\gamma$ is constructed that transfor…