Ergodic and combinatorial methods in fractal geometry

点击翻译按钮获取中文摘要

Fractal geometry includes the study of self-similar and self-affine sets, sets arising from dynamics and in general any sets (usually in Euclidean spaces) forwhich Hausdorff/packing dimension is an interesting property. Many recent advances about self-similar and self-affine sets use ideas and methods fromergodic theory; many solved an unsolved problems in combinatorics (discrete geometry) have interesting counterparts in fractal geometry. A main part of theproposed research will focus on self-similar sets and a version of the tube-null property, aiming at finding efficient coverings of self-similar sets with a smallnumber of narrow tubes and investigating the consequences for certain biLipschitz invariants. This research fits in the Mathematical Analysis research area, wholly within the Mathematical Sciences theme.