多复变与复几何研讨班：The Conformal Dimension and Minimality of Stochastic Objects

中科院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

学术报告

多复变与复几何研讨班

报告人: 李文博 博士（北京国际数学研究中心）

题  目：The Conformal Dimension and Minimality of Stochastic Objects

时  间：2024.11.12（星期二）14:30-15:30

地  点：南楼N913

摘  要：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(UToronto) and Hrant Hakobyan(KSU)。