Explore the Schramm-Loewner evolution (SLEκ) with a focus on the critical value κ=4 in this 44-minute lecture by Jason Miller at the Hausdorff Center for Mathematics. Delve into the proof that the range of an SLE_4 curve is almost surely conformally removable, a result with significant implications for the conformal welding of independent critical Liouville quantum gravity (LQG) surfaces. Learn about a new sufficient condition for conformal removability of sets in the complex plane, applicable beyond the boundaries of simply connected domains. Discover how this theorem extends to SLEκ curves for κ∈(4,8) under specific conditions. No prior knowledge of SLE or LQG is required to engage with this in-depth exploration of conformal geometry and stochastic processes.