# Lukas Schoug: Regularity of the SLE_4 uniformizing map and the SLE_8 trace

Time: Thu 2021-09-16 15.15 - 16.15

Location: 3418, Lindstedtsvägen 25, KTH Matematik

Lecturer: Lukas Schoug (Cambridge)

The Schramm–Loewner evolution (SLE) is a one-parameter family of random planar fractal curves, which has been of considerable interest since their introduction by Schramm in 1999, as they arise as scaling limits in several two-dimensional statistical mechanics models at criticality. Choosing the parameter $$\kappa$$ to be either 4 or 8 results in special behaviour, as $$\kappa = 4\; (\kappa = 8)$$ is the largest (resp. smallest) $$\kappa$$ such that $$\mathrm{SLE}_\kappa$$ curves are simple (resp. space-filling). As such, regularity results in those cases differ significantly from the cases of other values of $$\kappa$$. We will discuss recent results on the modulus of continuity of the $$\mathrm{SLE}_4$$ uniformizing map and the $$\mathrm{SLE}_8$$ trace, as well as a byproduct of our analysis, concerning the conformal removability of $$\mathrm{SLE}_4$$. The talk is based on joint work with Konstantinos Kavvadias and Jason Miller.

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Last changed: Sep 10, 2021