My research 

The majority of my work is in areas related to Dynamical Systems, Fractal Geometry and Number Theory. I am also interested in questions related to growth of matrix products.

For the complete list of my papers and preprints to date (all of which are downloadable), click here.

My research profiles: Google Scholar, MathSciNet, Research Gate.

Here are some topics I am (or have been) working on:

  1. Beta-expansions and other arithmetic representations of real numbers in non-integer bases;

  2. Bernoulli convolutions and other singular measures of arithmetic nature;

  3. Open dynamical systems (aka “maps with holes”)

  4. Joint spectral radius and the Finitemess Conjecture;

  5. Iterated function systems (IFSs) and their applications to digital channels;

  6. Fractals;

  7. Pisot numbers;

  8. Arithmetic codings of ergodic transformations of algebraic origin;

  9. Sum-of-digit functions and other summatory functions.

An overview of some of these topics can be found in my recent lecture course as well as my old survey paper Arithmetic Dynamics.

I am a former student and co-author of Anatoly Vershik. Below is the alphabetic list of my other collaborators:

Jean-Paul Allouche (Institut Mathématique de Jussieu)

Kevin Hare (University of Waterloo)

Simon Baker (University of Warwick)

James Montaldi (The University of Manchester)

David Broomhead

Ian Morris (University of Surrey)

Matthew Clarke (Deutsche Bank)

Matthew Nicol (University of Houston, Texas)

Jean-Marie Dumont

Eric Olivier (LATP, Marseille) 

De-Jun Feng (Chinese University of Hong Kong)

Boris Solomyak (Bar-Ilan)

Paul Glendinning (The University of Manchester)

Jacques Theys (BNP Paribas Fortis Bank, Brussels)

Alain Thomas (LATP, Marseille) 


My Erdös number is 3, via Vershik (2) and Freiman (1) – or Allouche (2) and Shallit (1).

My H-index is 18 (Google Scholar).