The Conformal Dimension and Minimality of Stochastic Objects
发布时间：2025年03月18日
浏览次数：82
发布者: He Liu
主讲人： 李文博（数学中心）
活动时间： 从 2025-03-24 15:00 到 16:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
The conformal dimension of a metric space is the infimum of the Hausdorff dimension among all its quasisymmetric images. We develop tools related to the Fuglede modulus to study the conformal dimension of stochastic spaces. We first construct the Bedford-McMullen type sets, and show that Bedford-McMullen sets with uniform fibers are minimal for conformal dimension. We further develop this line of inquiry by proving that a "natural" stochastic object, the graph of the one dimensional Brownian motion, is almost surely minimal. If time permits, I will also explore further developments related to Schramm-Loewner evolution (SLE), conformal loop ensembles (CLE), and related questions motivated by an exploration of the renowned Sullivan dictionary. This is a joint work with Ilia Binder and Hrant Hakobyan.
