Convergence of resistances on generalized Sierpinski carpets
报告人： Shiping Cao（University of Hong Kong）
时间：2026-05-25 14:00-15:00
地点：智华楼四元厅-225
Abstract:
Brownian motions on generalized Sierpinski carpets were constructed by Barlow and Bass as scaling limits of constant time-changed reflected Brownian motions on Euclidean domains approximating the carpet. In this talk, we show that the time scaling can be chosen in the form $\lambda^n$ for some $\lambda > 0$. Our proof is based on the Mosco convergence method, and at the same time, we give a positive answer to the open question of Barlow and Bass concerning the convergence of the renormalized effective resistance between opposite faces of the approximation domains.
This is joint work with Zhen-Qing Chen.
About the Speaker:
Shiping Cao is a Research Assistant Professor at the University of Hong Kong. His research focuses on Dirichlet forms on metric measure spaces, with a particular emphasis on fractals. He received his Ph.D. from Cornell University, where he was advised by Professor Robert S. Strichartz. From 2022 to 2025, he was a postdoctoral scholar at the University of Washington.
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