Alex Gorodnik: Quantitative ergodic theorems and Diophantine approximation
We investigate the problem of Diophantine approximation on rational surfaces using ergodic-theoretic techniques. It turns out that this problem is closely related to the asymptotic distribution of orbits for a suitably constructed dynamical system. Using this connection we establish analogues of Khinchin's and Jarnik's theorems in our setting. This is a joint work with A.Ghosh and A.Nevo.