beat365中国在线体育学术报告

--- 分析与偏微分方程讨论班(2023秋季第11讲)

The Conformal Dimension and Minimality of Stochastic Objects

李文博 博士

(北京大学)

时间与地点：10月31日（周1）10:00-11:00（北京时间);

沙河国实E602

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, we will discuss further developments on random spaces.

报告人简介: 李文博为北京大学北京国际数学研究中心的博士后研究员。他在2022年于多伦多大学获得博士学位，博士导师为Ilia Binder。他的研究领域为度量测度空间分析，度量几何和随机几何。

邀请人：朱政

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