In dynamics, I am interested in substitutions and tiling systems, especially in their spectral properties. Tilings (such as the Penrose tiling) are used as models of quasicrystals. Roughly speaking, quasicrystals are solids with a diffraction pattern typical for crystals, but which is incompatible with a periodic structure.

Selected bibliography

Fractals in the plane with positive length and zero Buffon needle probability (with Y. Peres and K. Simon), American Mathematical Monthly 110 (2003), 314--325.

Consequences of pure point diffraction spectra for multiset substitution systems (with J.-Y. Lee and R. V. Moody), Discrete and Computational Geometry 29 (2003), 525--560.

Spectra of Bernoulli convolutions as multipliers in L ^p on the circle (with N. Sidorov), Duke Math. Journal 120 (2003), 353--370.

Dynamics of self-similar tilings, Ergodic Theory and Dynamical Systems 17 (1997), 695--738.

On the random series ∑± λⁿ (an Erdös problem), Annals of Math. 142 (1995), 611--625.

Finite beta-expansions (with C. Frougny), Ergodic Theory and Dynamical Systems 12 (1992), 713--723.