The Geometry of Fractal Percolation and Randomly Perturbed Self-Affine Sets
Date:
Friday, 16 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 C1 mappings. Finally, we study the existence of interior points in randomly perturbed self-similar sets.
Poster:
