Ergodic and combinatorial methods in fractal geometry

Lead Research Organisation: University of Warwick
Department Name: Mathematics


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.


10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/V520226/1 30/09/2020 31/10/2025
2443767 Studentship EP/V520226/1 04/10/2020 04/10/2024 William O'Regan