Metric Diophantine approximation and dynamical systems

The introductory part will feature: rate of approximation of real numbers by rationals; theorems of Kronecker, Dirichlet, Liouville, Borel-Cantelli; connections with dynamical systems: circle rotations, hyperbolic flow in the space of lattices, geodesic flow on the modular survace, Gauss map (continued fractions); ergodicity, unique ergodicity, mixing, applications to uniform distribution of sequences (e.g. fractional parts of polynomials), Khinchin’s Theorem and the method of regular systems.