I am interested in the intersection of dynamical systems, ergodic theory and fractal geometry.  I am particularly interested in using analytical tools inspired by physics (eg thermodynamic formalism, theory of electrical networks etc) to study problems in these areas.

Four topics I am currently particularly interested in are: parabolic dynamics, stopping times, random matrix products and multifractal analysis. See my meta-web for an informal description of my perspective on these themes and some relevant collaborators.

Submitted:
Hausdorff dimension of the Rauzy gasket.
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‍Accepted/published:
‍Cover times in dynamical systems (with M. Todd). To appear in Israel Journal of Mathematics.
‍Parabolic carpets (with J. Fraser). To appear in Israel Journal of Mathematics.
‍Non-existence of the box dimension for dynamically invariant sets. To appear in Analysis & PDE.
‍Box dimensions of $(\times m, \times n)$-invariant sets (with J. Fraser). To appear in Indiana University Mathematics Journal.
‍On the convergence rate of the chaos game (with B. Bárány and I. Kolossváry). To appear in IMRN.
‍The Hausdorff dimension of self-projective sets (with A. Christodoulou). To appear in Transactions of the AMS.
‍Ledrappier-Young formulae for a family of non-linear attractors (with L. Lee). To appear in Math Zeitschrift.
‍How long is the Chaos Game? (with I. Morris). To appear in Bulletin of the LMS.
‍Dimension spectrum of infinite self-affine iterated function systems. To appear in Selecta Mathematica.
‍The box dimensions of exceptional self-affine sets in $\mathbb{R}^3$ (with J. Fraser). To appear in Advances in Mathematics.
‍Approximating integrals with respect to stationary probability measures of iterated function systems (with I. Cipriano). To appear in Ergodic Theory and Dynamical Systems.
‍Maximising measures and dimension gaps for countable branched systems (with S. Baker). To appear in Ergodic Theory and Dynamical Systems.
‍Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone (with I. Morris). Nonlinearity 33.4 (2020) 1572–1593.
‍Effective estimates on the top Lyapunov exponents for random matrix products (with I. Morris). Nonlinearity 32.11 (2019) 4117–4146.
‍A new proof of the dimension gap for the Gauss map. To appear in Mathematical Proceedings of the Cambridge Philosophical Society.
‍Dimensions of equilibrium measures on a class of planar self-affine sets (with J. Fraser and T. Jordan).  Journal of Fractal Geometry 7.1 (2020) 87-111.
‍Self-affine sets with non-compactly supported random perturbations (with T. Jordan).  Ann. Acad. Sci. Fen. Math. 39 (2014) 771-785.

Expository:
Quantitative covering and equidistribution. Submitted to the conference proceedings of On the Interface of Geometric Measure Theory and Fractal Geometry.
‍‍Self-projective sets, with A. Christodoulou. Conference proceedings of Fractals and Related Fields 4.
‍Fifty Years of Thermodynamic Formalism. Newsletter of the LMS, 483 (July 2019) 22-26.
‍Thermodynamic Formalism and Dimension gaps.. PhD thesis, University of Warwick, 2018.