My research

The majority of my work is in areas related to Dynamical Systems, Number Theory and Geometric Measure Theory. Recently I got 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 profile on Google Scholar is here.

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. Joint spectral radius and the Finitemess Conjecture;
4. Iterated function systems (IFSs) and their applications to digital channels;
5. Fractals;
6. Dimension theory;
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 (University Paris-6)
• Simon Baker (The University of Manchester)
• David Broomhead (The University of Manchester)
• Matthew Clarke (Cambridge University)
• Jean-Marie Dumont †
• De-Jun Feng (Chinese University of Hong Kong)
• Paul Glendinning (The University of Manchester)
• Kevin Hare (University of Waterloo)
• James Montaldi (The University of Manchester)
• Ian Morris (University of Surrey)
• Matthew Nicol (University of Houston, Texas)
• Eric Olivier (LATP, Marseille) 
• Boris Solomyak (University of Washington, Seattle)
• 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 15 (Google Scholar).