报告人：邱华（南京大学）

邀请人：徐剑

报告时间：2021年6月4日（星期五）16：00-17：30

报告地点： 科技楼（南楼）702室

报告题目：Self-similar Dirichlet forms on some new fractals

报告摘要：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.

报告人简介：邱华，南京大学数学系教授，博导。研究方向为分形分析。多次应邀访问美国康奈尔大学和香港中文大学。在J. Funct. Anal.，Ergodic Theory Dynam. Systems等刊物发表论文20多篇，并主持了多项国家自然科学基金和省部级科研项目。