Recent progress in S-adic diophantine approximation

We study the measure theory of non-generic sets (from the Diophantine point of view) in manifolds via orbits of certain flows in an appropriate homogeneous space. We will talk about some new developments in Diophantine approximation in the S-adic set-up, where S is a finite set of valuations of rationals. The metric Diophantine approximation has seen a tremendous boost in the last two decades, especially after the breakthrough of Kleinbock and Margulis in 1998.