报告题目一：Self-similar Dirichlet form on pillow-type carpets

报告人：邱华 (南京大学)

报告时间：2026.4.5 晚上7：00-9：00

报告地点：数学院301

报告摘要：We give a short, self-contained analytic proof of the existence of self-similar Dirichlet forms on pillow-type carpets, a family of infinitely ramified fractals that includes the Sierpi´nski carpet. This work is joint with Shiping Cao and Yizhou Wang.

报告人简介：邱华，南京大学数学系教授、博士生导师。主要从事分析学、位势论、分形分析的研究，主持多项国家级、省部级自然科学基金项目，在Probab. Theory Related Fields, Adv. Math., J. Funct. Anal., Ergodic Theory Dynam. Systems, Potential Anal.等高水平学术期刊上发表论文四十余篇。

报告题目二：A non-canonical diffusion on the Sierpinski carpet

报告人：邱华 (南京大学)

报告时间：2026.4.6 晚上7：00-9：00

报告地点：数学院301

报告摘要：We constructed a diffusion process on the Sierpinski carpet that satisfies the sub-Gaussian heat kernel estimate with respect to the Euclidean metric and a non-standard self-similar measure. This work is joint with Shiping Cao and Bingshen Wang.

报告人简介：邱华，南京大学数学系教授、博士生导师。主要从事分析学、位势论、分形分析的研究，主持多项国家级、省部级自然科学基金项目，在Probab. Theory Related Fields, Adv. Math., J. Funct. Anal., Ergodic Theory Dynam. Systems, Potential Anal.等高水平学术期刊上发表论文四十余篇。

报告题目三：The growth of eigenfunction extrema on p.c.f. fractals

报告人：邱华 (南京大学)

报告时间：2026.4.7 晚上7：00-9：00

报告地点：数学院301

报告摘要：We study the growth of local extrema of Laplacian eigenfunctions on post-critically finite (p.c.f.) fractals. We establish the precise two-sided estimate $N(u)\asymp\lambda^{d_S/2}$ for the Sierpinski gasket, demonstrating that the complexity of eigenfunctions is governed by the spectral exponent $d_S$. This stands in sharp contrast to the general $\lambda^{(n-1)/2}$ law on smooth manifolds, with the attainment of the exponent $d_S/2$ reflecting the high symmetry of the underlying fractal. Our result reveals a distinct spectral-geometric phenomenon on singular spaces. This work is joint with Haoran Tian.

报告人简介：邱华，南京大学数学系教授、博士生导师。主要从事分析学、位势论、分形分析的研究，主持多项国家级、省部级自然科学基金项目，在Probab. Theory Related Fields, Adv. Math., J. Funct. Anal., Ergodic Theory Dynam. Systems, Potential Anal.等高水平学术期刊上发表论文四十余篇。