Short Talk: Haoyu Liu

We consider the Schramm-Loewner evolution (SLE_\kappa) for \kappa \in (4,8), which is the regime where the curve is self-intersecting but not space-filling. We show that there exists \delta_0>0 such that for \kappa \in (8 - \delta_0,8), the range of an SLE_\kappa curve almost surely contains a topological Sierpi\'nski carpet. Combined with a result of Ntalampekos (2021), this implies that SLE_\kappa is almost surely conformally non-removable in this parameter range. Our result also implies that for \kappa \in (8 - \delta_0,8), the adjacency graph of the complementary connected components of the SLE_\kappa curve is disconnected. Based on joint work in progress with Zijie Zhuang (UPenn).