Publications

These articles are freely available on arXiv; see the links below, or my complete arXiv author record.

Research Articles

Preprints:

  1. A. Banaji and H. Yu. Fourier transform of nonlinear images of self-similar measures: qualitative aspects, 2026, arXiv.
  2. A. Banaji, H. Chen, A. Rutar and W. Wang. Attainable forms of lower spectra, 2026, arXiv.
  3. S. Baker and A. Banaji. Self-similar and self-conformal measures with slow Fourier decay, 2026, arXiv.
  4. S. Baker, A. Banaji, D.-J. Feng, C.-K. Lai and Y. Xiong. Distinct dimensions for attractors of bi-Lipschitz iterated function systems, 2025, arXiv.
  5. A. Banaji and A. Rutar. Lower box dimension of infinitely generated self-conformal sets, 2024, arXiv.

Accepted:

  1. A. Banaji and H. Yu. Fourier transform of nonlinear images of self-similar measures: quantitative aspects, 2025, arXiv.
    To appear in Peking Mathematical Journal

Published:

  1. A. Banaji, J. M. Fraser, I. Kolossváry and A. Rutar. Assouad spectrum of Gatzouras–Lalley carpets, arXiv, DOI
    Advances in Mathematics 484 (2026), Article 110707.
  2. S. Baker and A. Banaji. Polynomial Fourier decay for fractal measures and their pushforwards, arXiv, DOI
    Mathematische Annalen 392 (2025), 209–261.
  3. A. Banaji, A. Rutar and S. Troscheit. Interpolating with generalized Assouad dimensions, arXiv, DOI
    Journal of Geometric Analysis 35 (2025), Article 270.
  4. A. Banaji and I. Kolossváry. Intermediate dimensions of Bedford–McMullen carpets with applications to Lipschitz equivalence, arXiv, DOI, poster
    Advances in Mathematics 449 (2024), Article 109735.
  5. A. Banaji and J. M. Fraser. Assouad type dimensions of infinitely generated self-conformal sets, arXiv, DOI
    Nonlinearity 37 (2024), Article 045004.
  6. A. Banaji. Generalised intermediate dimensions, arXiv, DOI
    Monatshefte für Mathematik 202 (2023), 465–506.
  7. A. Banaji. Metric spaces where geodesics are never unique, arXiv, DOI
    American Mathematical Monthly 130 (2023), 747–754.
  8. A. Banaji and J. M. Fraser. Intermediate dimensions of infinitely generated attractors, arXiv, DOI
    Transactions of the American Mathematical Society 376 (2023), 2449–2479.
  9. A. Banaji and H. Chen. Dimensions of popcorn-like pyramid sets, arXiv, DOI
    Journal of Fractal Geometry 10 (2023), 151–168.
  10. A. Banaji and A. Rutar. Attainable forms of intermediate dimensions, arXiv, DOI
    Annales Fennici Mathematici 47 (2022), 939–960.

Collaborators

My co-authors to date are Alex Rutar, Simon Baker, Jonathan Fraser, Haipeng (Clarence) Chen, István Kolossváry, Han Yu, De-Jun Feng, Chun-Kit Lai, Sascha Troscheit, Wen Wang, Ying Xiong.

PhD Thesis

My PhD thesis, ‘Interpolating between Hausdorff and box dimension,’ studies a family of fractal dimensions known as the intermediate dimensions, which lie between the well-known Hausdorff and box dimensions. A two-page summary, Intermediate dimensions, appeared in the May 2024 issue of the Newsletter of the London Mathematical Society.

Master’s Dissertation

Solvability of partial differential equations on fractal domains