Dr Tony Samuel

School of Mathematics
Lecturer of Mathematics and Statistics

Contact details

Address
School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Tony is an Assistant Professor of Mathematics and Statistics at the University of Birmingham. He has held academic posts at California Polytechnic State University, Universität Bremen, Australian National University and the University of St Andrews. He has also had the privilege of holding prolonged research stays at the Hausdorff Research Institute for Mathematics, Humboldt–Universität zu Berlin, Institut Mittag–Leffler, and South China University of Technology. 

Since 2020 he has been a Fellow of the Higher Education Academy, and the Director of Student Experience for J-BJI – a joint institute which runs a transnational undergraduate education program. Further, in 2018 he was honoured with the Terrance Harris Excellence in Mentorship Award from California Polytechnic State University.

Tony's research interests esearch interests lie in aperiodic order (mathematical quasicrystals), Diophantine approximations, dynamical systems, fractal geometry, and numeration systems, and recently he has become interested in developing interactive educational materials using RStudio and the Python library Manim. For links to pre-prints of his research articles, as well as his peer reviewed publications, please visit arXiv and Google Scholar. Now and then, he also write reviews for MathSciNet and zbMATH.

Please see below, and his personal webpage, for further details on lecture courses Tony has taught, research projects and dissertations he has supervised, and articles he has published.

Personal webpage.

Qualifications

  • Fellow of the Higher Education Academy, Advance HE, 2020
  • PhD in Mathematics, University of St Andrews, 2011
  • BSc in Mathematics, University of St Andrews, 2005

Postgraduate supervision

Tony’s research is focussed on aperiodic order (mathematical quasicrystals), Diophantine approximations, dynamical systems, fractal geometry, and numeration systems, and recently he has become interested in developing interactive educational materials using RStudio and the Python library Manim. Enquiries from potential postdoctoral researchers, as well as research students and visitors, to work with him on any of these topics are always welcome.

Below is a selection of research projects and dissertations Tony has supervised.

Postdoctoral research projects supervised and co-supervised

  •  Deciphering the 3D structure of the epigenome for improved cancer diagnostics  Funded by SMQB – Seed Corn
  • Rauzy fractals of random substitutions – Part funded by DFG – SFB 1283

PhD dissertations supervised and co-supervised

  • Complexity of random substitutions (current) – Part funded by EPSRC
  • Finite and infinite rotation sequences and beyond
  • Fractal Martin boundaries (current) – Part funded by DFG – Sachbeihilfe
  • Measure–geometric Laplacians on the real line
  • Regularity of aperiodic subshifts

MSc dissertations supervised and co-supervised

  • Annihilating continued fractions
  • Diffusion on nested fractals
  • Entropy of the 1d–Greenberg–Hastings model
  • Fractals as Martin boundaries
  • Hausdorff dimension of graphs of Weierstraß functions
  • Hilbert’s curve and its friends
  • Intermediate β–shifts of finite type
  • Space filling curves
  • Spectral asymptotics of measure geometric Laplacians
  • The mass transference principle

Research

Tony's research interests centre around aperiodic order (mathematical quasicrystals), Diophantine approximations, dynamical systems, fractal geometry, and numeration systems, as well as mathematics education (inquiry based learning, and developing interactive educational materials using Manim and RStudio).

Publications

Books (Editor)

  • Marc Kesseböhmer, Sabrina Kombrink, Yakov Pesin, Tony Samuel and Jörg Schmeling (2021). Thermodynamic formalism. Stoch. Dyn. 21(3). ISSN 0219-4937.
  • Robert Niemeyer, Erin Pearse, John Rock and Tony Samuel (2019). Horizons of fractal geometry and complex dimensions. Contemp. Math. 731. ISBN 978-1-4704-3581-3.
  • Kurt Falk, Tobias Oertel-Jäger, Marc Kesseböhmer, Jens Rademacher and Tony Samuel (2017). Diffusion on fractals and non-linear dynamics. Discrete Contin. Dyn. Syst. Ser. S 10(2). ISSN 1937-1632.

Articles in print

  • Philipp Gohlke, Andrew Mitchell, Dan Rust and Tony Samuel. Measure theoretic entropy of random substitution subshifts. Ann. Henri Poincaré (to appear).
  • Marc Kesseböhmer, Sabrina Kombrink, Yakov Pesin, Tony Samuel and Jörg Schmeling. Preface: Thermodynamic formalism. Stoch. Dyn. 21(3),  1–5 (2021).
  • Zoe Cooperband, Erin Pearse, Blaine Quackenbush, Jordan Rowley, Tony Samuel and Matt West. Continuity of entropy of Lorenz maps. Indag. Math. (N.S.) 31(1), 96–105 (2020).
  • Marc Kesseböhmer, Tony Samuel and Karenina Sender. The Sierpiński gasket as the Martin boundary of a non–isotropic Markov chain. J. Fractal Geom. 7(2), 113–136 (2020).
  • Marc Kesseböhmer, Tony Samuel and Hendrik Weyer. Measure–geometric Laplacians on the real line. Comment. Math. Univ. Carolin. 61(3), 313–335 (2020).
  • Blaine Quackenbush, Tony Samuel and Matt West. Periodic intermediate β-expansions of Pisot numbers. Mathematics 8(903), 1–16 (2020).
  • Maik Gröger, Marc Kesseböhmer, Arne Mosbach, Tony Samuel and Malte Steffens. A classification of aperiodic order via spectral metrics and Jarnìk sets. Ergod. Dyn. Sys. 39(11), 3031–3065 (2019).
  • Marc Kesseböhmer, Arne Mosbach, Tony Samuel and Malte Steffens. Diffraction of return time measures. J. Stat. Phys. 174, 519–535 (2019).
  • Marc Kesseböhmer, Tony Samuel and Hendrik Weyer. Measure–geometric Laplacians for discrete distributions. Contemp. Math. 731, 133–142 (2019).
  • Sabrina Kombrink and Tony Samuel. Fractal geometry and dynamics. Lond. Math. Soc. Newsl. 481, 24–29 (2019).
  • Bing Li, Tuomas Sahlsten, Tony Samuel and Wolfgang Steiner. Denseness of intermediate β-shifts of finite type. Proc. Amer. Math. Soc. 147(5), 2045–2055 (2019).
  • Robert Niemeyer, Erin Pearse, John Rock and Tony Samuel. Preface: Horizons of fractal geometry and complex dimensions. Contemp. Math. 731, vii-x (2019).
  • Fabian Dreher, Marc Kesseböhmer, Arne Mosbach, Tony Samuel and Malte Steffens. Regularity of aperiodic minimal subshifts. Bull. Math. Sci. 8, 413–434 (2018).
  • Kurt Falk, Tobias Oertel-Jäger, Marc Kesseböhmer, Jens Rademacher and Tony Samuel. Preface: Diffusion on fractals and non–linear dynamics. Discrete Contin. Dyn. Syst. Ser. S 10(2), i–iv (2017).
  • Johannes Kautzsch, Marc Kesseböhmer and Tony Samuel. On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps. Ann. Henri Poincaré 17(9), 2585–2621 (2016).
  • Marc Kesseböhmer, Tony Samuel and Hendrik Weyer. A note on measure–geometric Laplacians. Monatsh. Math. 181, 643–655 (2016).
  • Bing Li, Tuomas Sahlsten and Tony Samuel. Intermediate β-shifts of finite type. Discrete Contin. Dyn. Syst. 36(1), 323–344 (2016).
  • Johannes Kautzsch, Marc Kesseböhmer, Tony Samuel and Bernd Stratmann. On the asymptotics of the α–Farey transfer operator. Nonlinearity 28(1), 143–166 (2015).
  • Fabian Dreher and Tony Samuel. Continuous images of Cantor’s ternary set. Amer. Math. Monthly 121(7), 640–643 (2014). Translated into Mandarin: Shu Xue Yi Lin 35(4), 381–384 (2016).
  • Tony Samuel, Nina Snigireva and Andrew Vince. Embedding the symbolic dynamics of Lorenz maps. Math. Proc. Camb. Phil. Soc. 156(3), 505–519 (2014).
  • Marc Kesseböhmer and Tony Samuel. Spectral metric spaces for Gibbs measures. J. Funct. Anal. 265(9), 1801–1828 (2013).
  • Tony Samuel. A simple proof of Vitali’s theorem for signed measures. Amer. Math. Monthly 120(7), 654–660 (2013).
  • Kenneth Falconer and Tony Samuel. Dixmier traces and coarse multifractal analysis. Ergod. Dyn. Sys. 31(2), 369–381 (2011).

Dissertations

  • Tony Samuel. A commutative noncommutative fractal geometry. University of St Andrews. PhD Thesis (2011).
  • Tony Samuel. Space filling curves and invariance of domain. University of St Andrews. BSc Thesis (2005).

View all publications in research portal