The Conformal Dimension and Minimality of Stochastic Objects
Time: 2025-03-18
Published By: He Liu
Speaker(s): Wenbo Li(BICMR)
Time: 15:00-16:00 March 24, 2025
Venue: Room 77201, Jingchunyuan 78, BICMR
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.
