Geodesic flow of the modular surface, continued fractions and Diophantine approximation, discrete subgroups of Lie groups, Dani correspondence and Schmidt games, Gauss map and Poincare sections, measured foliations and Teichmuller flows, Veech surfaces and Masur Divergence.

E-mail：yitwah@tsinghua.edu.cn

Familiarity with basic notions (group action, topological space, differential form, Riemann surface, Lebesgue measure) and a strong desire for a glimpse of their coordinated use in applications as opposed to development of general theory.

Einsiedler-Ward, Ergodic Theory with a view towards Number Theory, GTM 259

Masur-Tabachnikov, Rational billiards and flat structures, in Handbook of Dynamical Systems, Vol 1A