Publications

These articles are freely available on arXiv - see the links below, or here

Research Articles

Preprints:

  1. A. Banaji and H. Yu. Fourier transform of nonlinear images of self-similar measures: quantitative aspects, arXiv.
    Submitted.

  2. A. Banaji and A. Rutar. Lower box dimension of infinitely generated self-conformal sets, arXiv.
    Submitted.

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

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

Accepted:

  1. S. Baker and A. Banaji. Polynomial Fourier decay for fractal measures and their pushforwards, arXiv
    To appear in Mathematische Annalen

Published:

  1. A. Banaji and I. Kolossváry. Intermediate dimensions of Bedford–McMullen carpets with applications to Lipschitz equivalence, arXiv, poster
    Advances in Mathematics 449 (2024), 109735.

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

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

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

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

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

  7. 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 Alex Rutar (4), Jonathan Fraser (3), István Kolossváry (2), Simon Baker, Haipeng (Clarence) Chen, De-Jun Feng, Chun-Kit Lai, Sascha Troscheit, Ying Xiong, Han Yu.

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