Seminar| Institute of Mathematical Sciences
Time: Wednesday, October 21th, 2026,16:00-17:00
Location: IMS RS408
Speaker: Wenbo Li, Tsinghua University
Abstract: Random curves, fractals, and surfaces bring classical questions of complex analysis into a probabilistic setting. When do these spaces admit canonical geometric models, and which features of their geometry persist under controlled deformations. Quasisymmetric geometry provides a natural framework for studying these questions through uniformization, conformal dimension, and rigidity.
This talk surveys recent advances concerning Brownian motion, Schramm–Loewner evolution, and related random spaces. The emphasis will be on the geometric ideas behind the results and the connections between complex analysis and probability.
We will also explore how these developments suggest a third column devoted to random geometry in Sullivan’s dictionary between Kleinian groups and holomorphic dynamics, highlighting common questions and new research directions. The main concepts will be introduced for a broad mathematical audience.