Lie in Diophantine Approximation, a rapidly developing area of Analytic Number Theory. They are linked with a wide range of other topics including combinatorics on words, homogeneous dynamics, measure theory and ergodic theory. One of my most recent research activities is investigating the structure of the sets of badly approximable points in Rn and more generally in complete metric spaces. I am also investigating the approximational properties of Mahler numbers and Mahler functions.
