Tony Samuel

Colleges, School and Institutes

External positions

, Hausdorff Institute for Mathematics

26 Jan 20201 Mar 2020

Institut Mittag-Leffler

Sep 2017Dec 2017

Professor, California Polytechnic State University

Sep 2015Aug 2018

University of Bremen

Jan 2012Sep 2015

Australian National University (ANU)

Sep 2011Dec 2011

University of St Andrews

Oct 2010Sep 2011

Australian National University (ANU)

Apr 2010May 2010

Humboldt University of Berlin

Sep 2009

Research interests

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. Recent focus has been on applications of ergodic theory, noncommutative geometry and potential theory to fractals and quasicrystals, with a growing interest in linking these topics to other areas of mathematics, such as, geometric group theory, geometric measure theory and renewal theory.


Tony graduated from the University of St Andrews in 2005, and went on to complete a PhD in Pure Mathematics under the supervision of Prof. K. Falconer (University of St Andrews) and Prof. B. O. Stratmann (1957 - 2015), where he studied ways in which noncommutative geometry can be used to understand fractal sets. For his doctoral thesis, Tony was awarded an EPSRC Doctoral Prize, which funded a one year Postdoctoral Fellowship at the University of St Andrews. Following this, in 2011, he worked under the guidance of Prof. M. Barnsley (Austrilian National University) and Prof. A. Rennie (University of Wollongong) on ARC Discovery Project: DP0984353, where they studied noncommutative approaches to fractal geometry.

Subsequently, Tony has held posts at the University of Bremen as a Scientific Researcher (Wissenschaftlicher Mitarbeiter) and California Polytechnic State University as an Assistant Professor of Pure Mathematics. Further, in 2017 he spent a semester at Institut Mittag-Leffler where he took part in the research program Fractal Geometry and Dynamics led by Prof. K. Falconer, Prof. M. Järvenpää, Prof. A. Kupiainen, Prof. F. Ledrappier and Prof. P. Mattila; and is due to take part in the Trimester Progrm - Dynamics: Topology and Numbers, to be held at the Hausdorff Research Institute for Mathematics.

Tony's reseach has been published in leading mathematics journals, such as Ann. Henri Poincare, Bull. Math. Sci., Ergodic Theory Dynam. Systems, J. Funct. Anal. and Nonlinearity. He has been awarded 12 grants (total 687,000 EUR), as a lead investigator and within partnerships from UK funding bodies, such as EPSRC and the LMS, and foreign ones, including DFG and NSF.  He is also currently advising 2 PhD students and in 2018 he was the recipricant of the Terrance Harris Excellence in Mentorship Award from California Polytechnic State University.

Further, Tony initiated and was the main coordinator (2013 and 2015) for the annual Bremen winter school which celebrates its 7-th birthday in 2019, as well as the 2016 NSF summer school held at California Polytechnic State University and the 2017 memorial conference in honour of Prof. B. O. Stratman held at the Universität Bremen. In July 2019 and in June 2020, he will be co-organising two conferce at Institut Mittag Leffer.


PhD – Pure Mathematics – University of St Andrews, UK
Sept. 2006 – Aug. 2010
Dissertation: A commutative noncommutative fractal geometry
Supervisors: Prof. K. Falconer and Prof. B. O. Stratmann
Funding: EPSRC Doctoral Training Partnership (EP/P50273X/1)
Awards: EPSRC Doctoral Prize

BSc Hons.  Mathematics  University of St Andrews, UK
Sept. 2001 May 2005
Grade: First Class Hons.
Awards: Arthur Hinton Read Memorial Prize, Alexander Stewart Prize, D. E. Rutherford Prize, and Class Medal. (These awards are given to the highest performing student in BSc Pure and Applied Mathematics.)

Education/Academic qualification

  • Doctor of Philosophy, University of St Andrews

    A commutative noncommutative fractal geometry

    Sep 2006 - Aug 2010
  • Bachelor of Science, University of St Andrews

    Space Filling Curves and Invariance of Domain

    Sep 2001 - May 2005

Willingness to take PhD students


PhD projects

Aperiodic order; Diophantine approximations; Dynamical systems (symbolic and measure preserving); Ergodic theory (finite and infinite); Geometry (fractal, hyperbolic and noncommutative) and Stochastic processes