He is mainly interested in the interaction between dynamical systems, ergodic theory, and number theory. Relevant recent publications include: “A Solution to a Problem of Cassels and Diophantine Properties of Cubic Numbers” in Annals of Mathematics Volume173 (2011), and together with M. Einsiedler and L. Fishman, ”Diophantine Approximations on Fractals” in Geometric and Functional Analysis, Volume 21, Number 1.