报告人：邱华（南京大学）

日期：2020年11月20日

时间：16:30

地点：数统学院 LD202

摘要:The study of diffusion processes on fractals emerged as an independent research field in the late 80's. For p.c.f. self-similar sets Kigami showed that Dirichlet forms can be constructed as limits of electrical networks on approximation graphs. The construction relies on determining a proper form on the initial graph, whose existence and uniqueness in general is a difficult and fundamental problem in fractal analysis. In this talk, we consider the problem for three classes of fractals: 1. the Julia sets of Misiurewicz-Sierpinski maps; 2. the Sierpinski gasket with added rotational triangle; 3. the golden ratio Sierpinski gasket. The first ones come from complex dynamics which are not strictly self-similar sets. The second ones are due to Barlow which are not p.c.f. in general. The third one is a typical example which satisfies a graph-directed construction, but is not finitely ramified.

简介:邱华，男，南京大学数学系教授、博导。主要研究领域：分形分析与分形几何。主持和参加多项国家级、省部级科研项目，在J. Funct. Anal., Constr. Approx., Potential Anal., Ergod. Th. & Dynam. Sys., Nonlinearity, J. Fourier Anal. Appl. 等重要数学期刊上发表多篇研究论文。美国康奈尔大学数学系高级访问学者（2011.6-2012.6），美国数学会评论员。

联系人：罗军

欢迎广大师生积极参与！