Here is a list of my publications. You can also find lists on
MathSciNet,
the arXiv, zbMATH, and
Google Scholar.
Also see my author profile on MathSciNet.
At the bottom of the page you can find lists of survey articles, dissertations, and outreach publications. By following the arXiv links you can find pdfs of the papers.
My Erdös number is 3 via five disjoint paths (Fraser → Falconer → Croft → Erdös,  
Fraser → Pollicott → Preiss → Erdös,  
Fraser → Hare → Shallit → Erdös,  
Fraser → Lee → Vaughan → Erdös, Fraser → Simmons → Bergelson → Erdös) and my Erdös-Bacon number is +∞.
Preprints
81) On variants of the Furstenberg set problem, arXiv
        submitted.
80) Lp averages of the Fourier transform in finite fields, arXiv
        submitted.
79) Critical exponents and dimension for generalised limit sets (with T. Feng), arXiv
        submitted.
78) Fourier decay of product measures, arXiv
        submitted.
77) A Fourier analytic approach to exceptional set estimates for orthogonal projections (with A. E. de Orellana), arXiv
        submitted.
76) Obtaining the Fourier spectrum via Fourier coefficients (with M. Carnovale and A. E. de Orellana), arXiv
        submitted.
75) Assouad spectrum of Gatzouras-Lalley carpets (with A. Banaji, I. Kolossváry and A. Rutar), arXiv
        submitted.
74) Assouad type dimensions of parabolic Julia sets
(with L. Stuart), arXiv
        submitted.
To appear
73) The Fourier spectrum and sumset type problems, arXiv
        Mathematische Annalen (to appear).
72) Parabolic carpets (with N. Jurga), arXiv
        Israel Journal of Mathematics (to appear).
Published in 2024
71) A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra (with L. Stuart), arXiv
        Bulletin of the American Mathematical Society, 61, (2024), 103-118.
70) Assouad type dimensions of infinitely generated self-conformal sets (with A. Banaji), arXiv
        Nonlinearity, 37, (2024), Paper No. 045004.
69) Assouad-type dimensions of overlapping self-affine sets (with A. Rutar), arXiv
        Annales Fennici Mathematici, 49 (2024), 3-21.
2023
68) A nonlinear projection theorem for Assouad dimension and applications, arXiv
        Journal of the London Mathematical Society, 107, (2023), 777-797.
67) Intermediate dimensions of infinitely generated attractors (with A. Banaji), arXiv
        Transactions of the American Mathematical Society, 376, (2023), 2449-2479.
66) Box dimensions of (×m,×n)-invariant sets (with N. Jurga), arXiv
        Indiana University Mathematics Journal, 72, (2023), 2341-2367.
65) The Assouad dimension of self-affine measures on sponges (with I. Kolossváry), arXiv
        Ergodic Theory and Dynamical Systems, 43, (2023), 2974-2996.
64) Diophantine approximation in metric space (with H. Koivusalo and F. Ramírez), arXiv
        Bulletin of the London Mathematical Society, 55, (2023), 756-776.
63) Refined horoball counting and conformal measure for Kleinian group actions
(with L. Stuart), arXiv
        Annales Fennici Mathematici, 48, (2023), 325–344.
62) The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure
(with L. Stuart), arXiv
        Geometriae Dedicata, 217, (2023), Paper No. 1, 32 pp.
61) Dimensions of Kleinian orbital sets (with T. Bartlett), arXiv
        Journal of Fractal Geometry, 10, (2023), 267-278.
60) Minkowski dimension for measures (with K. J. Falconer & A. Käenmäki), arXiv
        Proceedings of the American Mathematical Society, 151, (2023), 779-794.
2022
59) On the Fourier dimension of (d,k)-sets and Kakeya sets with restricted directions (with T. Harris and N. Kroon), arXiv
        Mathematische Zeitschrift, 301, (2022), 2497-2508.
58) Dimensions of the popcorn graph (with H. Chen and H. Yu), arXiv
        Proceedings of the American Mathematical Society, 150, (2022), 4729-4742.
57) The fractal structure of elliptical polynomial spirals (with S. A. Burrell and K. J. Falconer), arXiv
        Monatshefte für Mathematik, 199, (2022), 1-22.
2021
56) The box dimensions of exceptional self-affine sets in ℝ3 (with N. Jurga), arXiv
        Advances in Mathematics, 385, (2021), 107734.
55) Lq-spectra of measures on planar non-conformal attractors (with K. J. Falconer and L. D. Lee), arXiv
        Ergodic Theory and Dynamical Systems, 41, (2021), 3288-3306.
54) Approximate arithmetic structure in large sets of integers (with H. Yu), arXiv
        Real Analysis Exchange, 46, (2021), 163-174.
53) The Assouad spectrum of random self-affine carpets (with S. Troscheit), arXiv
        Ergodic Theory and Dynamical Systems, 41, (2021), 2927-2945.
52) Assouad dimension influences the box and packing dimensions of orthogonal projections (with K. J. Falconer & P. Shmerkin), arXiv
        Journal of Fractal Geometry, 8, (2021), 247-259.
51) Lq-spectra of self-affine measures: closed forms, counterexamples, and split binomial sums (with L. D. Lee, I. D. Morris & H. Yu), arXiv
        Nonlinearity, 34, (2021), 6331-6357.
50) Regularity versus smoothness of measures (with S. Troscheit), arXiv
        Pacific Journal of Mathematics, 311, (2021), 257-275.
49) On Hölder solutions to the spiral winding problem, arXiv
        Nonlinearity, 34, (2021), 3251-3270.
48) Projection theorems for intermediate dimensions (S. A. Burrell & K. J. Falconer), arXiv
        Journal of Fractal Geometry, 8, (2021), 95-116.
47) Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions (with P. Shmerkin & A. Yavicoli), arXiv
        Journal of Fourier Analysis and Applications, 27, (2021).
46) Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images (with Á. Farkas, E. Nesharim & D. Simmons), arXiv
        Mathematika, 67, (2021), 196-213.
45) On Hölder maps and prime gaps (with H. Chen), arXiv
        Real Analysis Exchange, 46, (2021), 523--532.
2020
44) Intermediate dimensions (with K. J. Falconer & T. Kempton), arXiv
        Mathematische Zeitschrift, 296, (2020), 813-830.
43) Attainable values for the Assouad dimension of projections (with A. Käenmäki), arXiv
        Proceedings of the American Mathematical Society, 148, (2020), 3393-3405.
42) The dimensions of inhomogeneous self-affine sets (with S. A. Burrell), arXiv
        Annales Academiæ Scientiarum Fennicæ Mathematica, 45, (2020), 313-324.
41) On the upper regularity dimensions of measures (with D. C. Howroyd), arXiv
        Indiana University Mathematics Journal, 69, (2020), 685-712.
40) Dimensions of equilibrium measures on a class of planar self-affine sets (with T. Jordan & N. Jurga), arXiv
        Journal of Fractal Geometry, 7, (2020), 87-111.
2019
39) Regularity of Kleinian limit sets and Patterson-Sullivan measures, arXiv
        Transactions of the American Mathematical Society, 372, (2019), 4977-5009.
38) Dimension growth for iterated sumsets (with D. C. Howroyd & H. Yu), arXiv
        Mathematische Zeitschrift, 293, (2019), 1015-1042.
37) On the Hausdorff dimension of microsets (with D. C. Howroyd, A. Käenmäki & H. Yu), arXiv
        Proceedings of the American Mathematical Society, 147, (2019), 4921-4936.
36) Dimensions of sets which uniformly avoid arithmetic progressions (with K. Saito & H. Yu), arXiv
        International Mathematics Research Notices (IMRN), (2019), 4419-4430.
35) The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra (with K. E. Hare, K. G. Hare, S. Troscheit & H. Yu), arXiv
        Annales Academiæ Scientiarum Fennicæ Mathematica, 44, (2019), 379-387.
34) Inhomogeneous self-similar sets with overlaps (with S. Baker & Á. Máthé), arXiv
        Ergodic Theory and Dynamical Systems, 39, (2019), 1-18.
2018
33) Distance sets, orthogonal projections, and passing to weak tangents, arXiv
        Israel Journal of Mathematics, 226, (2018), 851-875.
32) Assouad type spectra for some fractal families (with H. Yu), arXiv
        Indiana University Mathematics Journal, 67, (2018), 2005-2043.
31) New dimension spectra: finer information on scaling and homogeneity (with H. Yu), arXiv
        Advances in Mathematics, 329, (2018), 273-328.
30) Arithmetic patches, weak tangents, and dimension (with H. Yu), arXiv
        Bulletin of the London Mathematical Society, 50, (2018), 85-95.
29) The Assouad dimension of randomly generated fractals (with J. J. Miao & S. Troscheit), arXiv
        Ergodic Theory and Dynamical Systems, 38, (2018), 982-1011.
28) Quantifying inhomogeneity in fractal sets (with M. Todd), arXiv
        Nonlinearity, 31, (2018), 1313-1330.
27) On the Lq Dimensions of Measures on Hueter-Lalley Type Self-Affine Sets (with T. Kempton), arXiv
        Proceedings of the American Mathematical Society, 146, (2018), 161-173.
26) On the Fourier analytic structure of the Brownian graph (with T. Sahlsten), arXiv
        Analysis & PDE, 11, (2018), 115-132.
2017
25) The Assouad dimensions of projections of planar sets (with T. Orponen), arXiv
        Proceedings of the London Mathematical Society, 114, (2017), 374-398.
24) The Assouad dimension of self-affine carpets with no grid structure (with T. Jordan), arXiv
        Proceedings of the American Mathematical Society, 145, (2017), 4905-4918.
23) Some results in support of the Kakeya conjecture (with E. J. Olson & J. C. Robinson), arXiv
        Real Analysis Exchange, 42, (2017), 253-268.
22) Uniform scaling limits for ergodic measures (with M. Pollicott), arXiv
        Journal of Fractal Geometry, 4, (2017), 1-19.
21) Assouad type dimensions for self-affine sponges (with D. Howroyd), arXiv
        Annales Academiæ Scientiarum Fennicæ Mathematica, 42, (2017), 149-174.
2016
20) On the Lq-spectrum of planar self-affine measures, arXiv
        Transactions of the American Mathematical Society, 368, (2016), 5579-5620.
19) On the dimensions of a family of overlapping self-affine carpets (with P. Shmerkin), arXiv
        Ergodic Theory and Dynamical Systems, 36, (2016), 2463-2481.
18) Inhomogeneous self-affine carpets, arXiv
        Indiana University Mathematics Journal, 65, (2016), 1547-1566.
2015
17) On the Assouad dimension of self-similar sets with overlaps (with A. M. Henderson, E. J. Olson & J. C. Robinson), arXiv
        Advances in Mathematics, 273, (2015), 188-214.
16) Micromeasure distributions and applications for conformally generated fractals (with M. Pollicott), arXiv
        Mathematical Proceedings of the Cambridge Philosophical Society, 159, (2015), 547-566.
15) First and second moments for self-similar couplings and Wasserstein distances, arXiv
        Mathematische Nachrichten, 288, (2015), 2028-2041.
14) Scaling scenery of (×m,×n) invariant measures (with A. Ferguson & T. Sahlsten), arXiv
        Advances in Mathematics, 268, (2015), 564-602.
13) On the equality of Hausdorff measure and Hausdorff content (with Á. Farkas), arXiv
        Journal of Fractal Geometry, 2, (2015), 403-429.
12) Remarks on the analyticity of subadditive pressure for products of triangular matrices, arXiv
        Monatshefte für Mathematik, 177, (2015), 53-65.
11) Dimension and measure for typical random fractals, arXiv
        Ergodic Theory and Dynamical Systems, 35, (2015), 854-882.
10) A note on the 1-prevalence of continuous images with full Hausdorff dimension (with J. T. Hyde), arXiv
        Journal of Mathematical Analysis and Applications, 421, (2015), 1713-1720.
2014
9) On Fourier analytic properties of graphs (with T. Orponen & T. Sahlsten), arXiv
        International Mathematics Research Notices (IMRN), (2014), 2730-2745.
8) Assouad type dimensions and homogeneity of fractals, arXiv
        Transactions of the American Mathematical Society, 366, (2014), 6687-6733.
2013
7) Dimension and measure for generic continuous images (with R. Balka, Á. Farkas & J. T. Hyde), arXiv
        Annales Academiæ Scientiarum Fennicæ Mathematica, 38, (2013), 389-404.
6) The visible part of plane self-similar sets (with K. J. Falconer), arXiv
        Proceedings of the American Mathematical Society, 141, (2013), 269-278.
2012
5) Inhomogeneous self-similar sets and box dimensions, arXiv
        Studia Mathematica, 213, (2012), 133-156.
4) On the packing dimension of box-like self-affine sets in the plane, arXiv
        Nonlinearity, 25, (2012), 2075-2092.
3) The Hausdorff dimension of graphs of prevalent continuous functions (with J. T. Hyde), arXiv
        Real Analysis Exchange, 37, (2011/2012), 333-352.
2011
2) Multifractal spectra of random self-affine multifractal Sierpiński sponges in ℝd (with L. Olsen)
        Indiana University Mathematics Journal, 60, (2011), 937-984.
1) The horizon problem for prevalent surfaces (with K. J. Falconer), arXiv
        Mathematical Proceedings of the Cambridge Philosophical Society, 151, (2011), 355-372.
Books and theses
• Assouad dimension and fractal geometry, arXiv, CUP, more
        CUP, Tracts in Mathematics Series, 222, (2020)
• Dimension theory and fractal constructions based on self-affine carpets, St Andrews DRR
        PhD thesis, The University of St Andrews, (2013).
Survey and expository articles
6) Inhomogeneous attractors and box dimension, arXiv
        invited article, Contemporary Mathematics
5) The Poincaré exponent and the dimensions of Kleinian limit sets, arXiv
        The American Mathematical Monthly, 129, (2022), 480--484.
4) Fractal geometry of Bedford-McMullen carpets, arXiv
        Proceedings of the Fall 2019 Jean-Morlet Chair programme, Springer Lecture Notes Series, 2021, (Eds. M. Pollicott & S. Vaienti).
3) Interpolating between dimensions, arXiv
        Fractal Geometry and Stochastics VI, Birkhäuser, Progress in Probability 76, 2021, (Eds. U. Freiberg, B. Hambly, M. Hinz & S. Winter).
2) Almost arithmetic progressions in the primes and other large sets, arXiv
        The American Mathematical Monthly, 126, (2019), 553-558.
1) Sixty Years of Fractal Projections (with K. J. Falconer & X. Jin), arXiv
        Fractal Geometry and Stochastics V, Birkhäuser, Progress in Probability 70, 2015, (Eds. C. Bandt, K. J. Falconer & M. Zähle).
Outreach publications
3) 2520 ants for Dylan,
        The Newsletter of the London Mathematical Society, 488, (2020), 28-30.
2) Logic puzzles with gnomes and hats,
        The Scottish Mathematical Council Journal, 45, (2015), 48-51.
1) Fractals in Lagganlia,
        The Scottish Mathematical Council Journal, 44, (2014), 58-60.
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