# The Geometry of Fractal Percolation and Randomly Perturbed Self-Affine Sets

Date:

Friday, 9 December, 2022 - 14:30 - 17:30

Venue:

LSB 222

Seminar Type:

Short Course

Speaker Name:

Prof. Karoly SIMON

Affiliation:

Budapest University of Technology and Economics & CUHK

Abstract:

In this short course we consider the geometric Measure theoretical properties of two families of random fractals: the Fractal percolation sets and the randomly perturbed self-affine sets.

Lectures 1-6: We study Fractal percolation sets from the point of their Hausdorff dimension, connectivity, existence of interval in projections, dimension of slices and rectifiability.

Lectures 7-10. We introduce the self-affine transversality condition for randomly perturbed self-affine sets. We extend this method to dominated triangular *C*^{1} mappings. Finally, we study the existence of interior points in randomly perturbed self-similar sets.

Poster: