Publications

These articles are freely available on arXiv - see the links below.

Research Articles

Preprints:

  1. S. Baker and A. Banaji. Polynomial Fourier decay for fractal measures and their pushforwards, arXiv
    Submitted.

  2. A. Banaji, J. M. Fraser, I. Kolossváry and A. Rutar. Assouad spectrum of Gatzouras–Lalley carpets, arXiv
    Submitted.

  3. A. Banaji, A. Rutar and S. Troscheit. Interpolating with generalized Assouad dimensions, arXiv
    Submitted.

Accepted:

  1. A. Banaji and I. Kolossváry. Intermediate dimensions of Bedford–McMullen carpets with applications to Lipschitz equivalence, arXiv, poster
    To appear in Advances in Mathematics

Published:

  1. A. Banaji and J. M. Fraser. Assouad type dimensions of infinitely generated self-conformal sets, arXiv
    Nonlinearity 37 (2024), 045004.

  2. A. Banaji. Generalised intermediate dimensions, arXiv
    Monatshefte für Mathematik 202 (2023), 465–506.

  3. A. Banaji. Metric spaces where geodesics are never unique, arXiv
    American Mathematical Monthly 130 (2023), 747–754.

  4. A. Banaji and J. M. Fraser. Intermediate dimensions of infinitely generated attractors, arXiv
    Transactions of the American Mathematical Society 376 (2023), 2449–2479.

  5. A. Banaji and H. Chen. Dimensions of popcorn-like pyramid sets, arXiv
    Journal of Fractal Geometry 10 (2023), 151–168.

  6. A. Banaji and A. Rutar. Attainable forms of intermediate dimensions, arXiv
    Annales Fennici Mathematici 47 (2022), 939–960.

Collaborators

My co-authors to date are Jonathan Fraser (3), Alex Rutar (3), István Kolossváry (2), Simon Baker (1), Haipeng Chen (Clarence) (1), Sascha Troscheit (1)

PhD Thesis

A main focus of my PhD thesis is a family of fractal dimensions, known as the intermediate dimensions, which lie between the well known Hausdorff and box dimensions. The full thesis, entitled ‘Interpolating between Hausdorff and box dimension,’ can be found here. A two-page ‘microthesis,’ published in the May 2024 edition of the Newsletter of the London Mathematical Society and entitled ‘Intermediate dimensions,’ can be found here.

Master’s Dissertation

Solvability of partial differential equations on fractal domains