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 +∞.
74) The Fourier dimension spectrum and sumset type problems, arXiv
submitted.
73) Assouad-type dimensions of overlapping self-affine sets (with A. Rutar), arXiv
submitted.
72) Assouad type dimensions of infinitely generated self-conformal sets (with A. Banaji), arXiv
submitted.
71) Assouad type dimensions of parabolic Julia sets
(with L. Stuart), arXiv
submitted.
70) A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra (with L. Stuart), arXiv
Bulletin of the American Mathematical Society (to appear).
69) Parabolic carpets (with N. Jurga), arXiv
Israel Journal of Mathematics (to appear).
68) Dimensions of Kleinian orbital sets (with T. Bartlett), arXiv
Journal of Fractal Geometry (to appear).
67) The Assouad dimension of self-affine measures on sponges (with I. Kolossváry), arXiv
Ergodic Theory and Dynamical Systems (to appear).
66) Box dimensions of (×m,×n)-invariant sets (with N. Jurga), arXiv
Indiana University Mathematics Journal (to appear).
65) Diophantine approximation in metric space (with H. Koivusalo and F. Ramírez), arXiv
Bulletin of the London Mathematical Society, 55, (2023), 756-776.
64) A nonlinear projection theorem for Assouad dimension and applications, arXiv
Journal of the London Mathematical Society, 107, (2023), 777-797.
63) Intermediate dimensions of infinitely generated attractors (with A. Banaji), arXiv
Transactions of the American Mathematical Society, 376, (2023), 2449-2479.
62) Refined horoball counting and conformal measure for Kleinian group actions
(with L. Stuart), arXiv
Annales Fennici Mathematici, 48, (2023), 325–344.
61) The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure
(with L. Stuart), arXiv
Geometriae Dedicata, 217, (2023), Paper No. 1, 32 pp.
60) Minkowski dimension for measures (with K. J. Falconer & A. Käenmäki), arXiv
Proceedings of the American Mathematical Society, 151, (2023), 779-794.
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.
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.
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.
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.
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.
25) 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.
24) The Assouad dimensions of projections of planar sets (with T. Orponen), arXiv
Proceedings of the London Mathematical Society, 114, (2017), 374-398.
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.
20) On the dimensions of a family of overlapping self-affine carpets (with P. Shmerkin), arXiv
Ergodic Theory and Dynamical Systems, 36, (2016), 2463-2481.
19) On the Lq-spectrum of planar self-affine measures, arXiv
Transactions of the American Mathematical Society, 368, (2016), 5579-5620.
18) Inhomogeneous self-affine carpets, arXiv
Indiana University Mathematics Journal, 65, (2016), 1547-1566.
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.
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.
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.
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.
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
• Assouad dimension and fractal geometry, arXiv, CUP
CUP, Tracts in Mathematics Series, 222, (2020)
Survey and expository articles
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).
Dissertations
• Dimension theory and fractal constructions based on self-affine carpets, St Andrews DRR
PhD thesis, The University of St Andrews, (2013).
Supervisors: Kenneth Falconer and Lars Olsen.
• Multifractals and irregular measures on the middle third Cantor set,
MMath dissertation, The University of St Andrews, (2009).
Supervisor: Kenneth Falconer.
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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