Schramm-Loewner evolution contains a topological Sierpiński carpet when $\kappa$ is close to 8

Organizers

吴昊，杨帆，姜建平，顾陈琳，李文博

Speaker

刘浩宇 北京大学

Time

Thur., 16:00 - 17:00

Dec. 18, 2025

Venue

C548, Shuangqing Complex Building

Schramm-Loewner evolution contains a topological Sierpiński carpet when $\kappa$ is close to 8

Schramm-Loewner evolution (SLE$_\kappa$) is a one-parameter family of random fractal curves that describes the scaling limits of interfaces in two-dimensional statistical mechanics models. This talk will present a result showing that there exists $\delta>0$ such that for $\kappa \in (8 - \delta, 8)$, the range of an SLE$_\kappa$ curve almost surely contains a topological Sierpiński carpet. Combined with a result of Ntalampekos (2021), this implies that in this parameter range, SLE$_\kappa$ is almost surely conformally non-removable, and the conformal welding problem for SLE$_\kappa$ does not have a unique solution. Our result also implies that for $\kappa \in (8 - \delta, 8)$, the adjacency graph of the complementary connected components of the SLE$_\kappa$ curve is disconnected. This is joint work with Zijie Zhuang (UPenn).