Ergodic and combinatorial methods in fractal geometry
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
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.
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.
Organisations
People |
ORCID iD |
Andras Mathe (Primary Supervisor) | |
William O'Regan (Student) |
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 | 03/07/2024 | William O'Regan |