Fractal Geometry and Analysis
Fractals are highly non-smooth sets that often possess self-similarity, infinite irregularity, and non-integral Hausdorff dimension. They arise naturally in many branches of mathematics, science, and engineering. This is an introductory course. The first part of this course (10 weeks) covers the following core topics: Hausdorff measure and dimension, packing measure and dimension, box dimension, the collage theorem, iterated function systems, self-similar sets, the Moran-Hutchinson theorem, self-similar measures. The second part of this course (6 weeks) will survey several research-oriented topics. Based on students' interests, the topics will be selected from the following list: the multifractal formalism, the Laplacian and analysis on fractals, fractals in Riemannian manifolds.
讲师
日期
2026年02月26日 至 05月14日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周四 | 13:30 - 16:55 | Shuangqing | ZOOM 07 | 559 700 6085 | BIMSA |
视频公开
公开
笔记公开
公开
讲师介绍
Dr. Ngai received his B.Sc. from University of Hong Kong, and his M.A. and Ph.D. from University of Pittsburgh. After receiving his Ph.D., he has held research and teaching positions at The Chinese University of Hong Kong, Cornell University, Georgia Institute of Technology, and Georgia Southern University. He joined Beijing Institute of Mathematical Sciences and Applications as a professor in 2024. His main research areas are fractal geometry and the theory of fractal measures. He is also interested in the theories of wavelets, self-affine tiles, fractal differential equations, and spectral graph theory.