Ergodic and combinatorial methods in fractal geometry

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) for
which Hausdorff/packing dimension is an interesting property. Many recent advances about self-similar and self-affine sets use ideas and methods from
ergodic theory; many solved an unsolved problems in combinatorics (discrete geometry) have interesting counterparts in fractal geometry. A main part of the
proposed 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 small
number 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.