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Presented By: Probability and Analysis Seminar - Department of Mathematics

Probability and Analysis Seminar: Conformal removability and bubble connectivity of non-simple SLE

Haoyu Liu (PKU/MIT)

Schramm-Loewner evolution (SLE_\kappa) is a one-parameter family of random fractal curves arising as scaling limits of interfaces in two-dimensional statistical mechanics models. For \kappa \in (4, 8), the SLE_\kappa curve is self-intersecting but not space-filling, forming complementary connected components known as bubbles. In this talk, I will discuss the relationship between the conformal removability of SLE traces and connectivity of the bubble adjacency graph, as well as a sharp phase transition as \kappa varies. Joint work with Zijie Zhuang (UNIGE).

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