Here is a list of my publications. You can also find lists on MathSciNet, the arXiv or Google Scholar. Also see my author profile on MathSciNet. At the bottom of the page you can find a list of non-research publications and dissertations.
19) Some results in support of the Kakeya conjecture (with E. J. Olson & J. C. Robinson), arXiv
submitted.
18) On the dimensions of a family of overlapping self-affine carpets (with P. Shmerkin), arXiv
submitted.
17) On the Assouad dimension of self-similar sets with overlaps (with A. M. Henderson, E. J. Olson & J. C. Robinson), arXiv
submitted.
16) First and second moments for self-similar couplings and Wasserstein distances, arXiv
submitted.
15) Remarks on the analyticity of subadditive pressure for products of triangular matrices, arXiv
submitted.
14) Scaling scenery of (×m,×n) invariant measures (with A. Ferguson & T. Sahlsten), arXiv
submitted.
13) Inhomogeneous self-affine carpets, arXiv
submitted.
12) On the Lq-spectrum of planar self-affine measures, arXiv
Transactions of the American Mathematical Society (to appear).
11) A note on the 1-prevalence of continuous images with full Hausdorff dimension (with J. T. Hyde), arXiv
Journal of Mathematical Analysis and Applications (to appear).
10) Assouad type dimensions and homogeneity of fractals, arXiv
Transactions of the American Mathematical Society (to appear).
9) Dimension and measure for typical random fractals, arXiv
Ergodic Theory and Dynamical Systems (to appear).
8) On Fourier analytic properties of graphs (with T. Orponen & T. Sahlsten), arXiv
International Mathematics Research Notices (IMRN), (2014), 2730-2745.
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.
Non-research publications:
• Fractals in Lagganlia,
The Scottish Mathematical Council Journal, Invited article (to appear), (2014).
Dissertations:
• Dimension theory and fractal constructions based on self-affine carpets, St Andrews DRR
PhD thesis, The University of St Andrews, (2013).
• Multifractals and irregular measures on the middle third Cantor set,
MMath dissertation, The University of St Andrews, (2009).
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