Course description:

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, Hausdorff dimension of self-similar sets with overlaps, the Laplacian and analysis on fractals, self-affine tilings, complex dynamical systems and the Mandelbrot set, and fractals in Riemannian manifolds.

Prerequisite: undergraduate analysis

Personal Website：https://scholars.georgiasouthern.edu/en/persons/sze-man-ngai-2 

Registration: https://www.wjx.top/vm/YqWq7TM.aspx#