IS05: Random Planar Geometry
Organizer: Wei Qian (City University of Hong Kong)
Schramm-Loewner evolution contains a topological Sierpi'nski carpet when \(\kappa\) is close to 8
Zijie Zhuang
In this talk, I will present a result showing 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 Sierpiński carpet. Combined with a result of Ntalampekos (2021), this implies that SLE\(_\kappa\) is almost surely conformally non-removable in this parameter range. I will explain the main intuition coming from Mandelbrot’s fractal percolation and discuss some open questions. Based on joint work with Haoyu Liu (PKU).