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Research Interests

My research interests include aperiodic order, Diophantine approximations, dynamical systems (symbolic and measure preserving), ergodic theory (finite and infinite), geometry (fractal, hyperbolic and noncommutative) and Markov chains. Recently, my focus has been on applications of ergodic theory, noncommutative geometry and potential theory to fractals and quasicrystals. I am also very interested in linking these topics to other areas of mathematics, such as, geometric group theory, geometric measure theory and renewal theory, as well as, the application and development of novel mathematical methods/theories.

Books (Editor)

  1. Diffusion on Fractals and Non-linear Dynamics: Discrete Contin. Dyn. Syst. Ser. S 10(2), 161-394 (2017).
    Editors: K. Falk, T. Jäger, M. Kesseböhmer, J. Rademacher and T. Samuel.
  2. Horizons of Fractal Geometry and Complex Dimensions. Contemp. Math. (Expected publication year 2018).
    Editors: R. G. Niemeyer, E. P. J. Pearse, J. A. Rock and T. Samuel.


  1. B. Li, T. Sahlsten, T. Samuel and W. Steiner. On the density of intermediate β-shifts of finite type: In Review. Pre-print: arXiv:1709.08035.
  2. M. Kesseböhmer, A. Mosbach, T. Samuel and M. Steffens. Diffraction of return time measures: In Review. Pre-print: arXiv:1801.07608.
  3. M. Kesseböhmer, T. Samuel and H. Weyer. Measure-geometric Laplacians on the real line: In Review. Pre-print: arXiv:1802.04858.


  1. T. Samuel. A commutative noncommutative fractal geometry: Ph.D. Thesis, University of St Andrews (2011).
  2. K. Falconer and T. Samuel. Dixmier traces and coarse multifractal analysis: Ergod. Dyn. Sys. 31, 369-381 (2011).
  3. T. Samuel. A simple proof of Vitali's theorem for signed measures: Amer. Math. Monthly 120(7), 654-660 (2013).
  4. M. Kesseböhmer and T. Samuel. Spectral metric spaces for Gibbs measures: J. Funct. Anal. 31, 1801-1828 (2013).
  5. T. Samuel, N. Snigireva and A. Vince. Embedding the symbolic dynamics of Lorenz maps: Math. Proc. Camb. Phil. Soc. 156(3), 505-519 (2014).
  6. F. Dreher and T. 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).
  7. J. Kautzsch, M. Kesseböhmer, T. Samuel and B. O. Stratmann. On the asymptotics of the α-Farey transfer operator: Nonlinearity 28, 143-166 (2015).
  8. J. Kautzsch, M. Kesseböhmer and T. Samuel. On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps: Ann. Henri Poincaré 17(9), 2585-2621 (2016).
  9. B. Li, T. Sahlsten and T. Samuel. Intermediate β-shifts of finite type: Discrete Contin. Dyn. Syst. 36(1), 323-344 (2016).
  10. M. Kesseböhmer T. Samuel and H. Weyer. A note on measure-geometric Laplacians: Monatsh. Math. 181(3), 643-655 (2016).
  11. F. Dreher, M. Kesseböhmer, A. Mosbach, T. Samuel and M. Steffens. Regularity of aperiodic minimal subshifts: Bull. Math. Sci. 1-22 (2017).
  12. M. Kesseböhmer, T. Samuel and H. Weyer. Measure-geometric Laplacians for discrete distributions: Accepted for publication in Contemp. Math. 8 pages (2017).
  13. M. Gröger, M. Kesseböhmer, A. Mosbach, T. Samuel and M. Steffens. A classification of aperiodic order via spectral metrics and Jarnìk sets: Accepted for publication in Ergod. Dyn. Sys. 38 pages (2018).
  14. M. Kesseböhmer, T. Samuel and K. Sender. The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain: Accepted for publication in J. Fractal Geom. 21 pages (2018).