Francois Ballay, Beijing International Center for Mathematical Research (BICMR) Peking University. Beijing.
Middle Lecture Room, Math Building
The fundamental problem in Diophantine approximation is to know how closely an irrational number can be approximated by a rational number. I will describe how this question can be generalized to the case of closed points on a projective variety defined over a number field. In particular, I will present an effective Liouville type Theorem, which gives an explicit upper bound for the height of rational points that are close to a given algebraic point of the variety. The main result is an effective version of a recent Theorem of David McKinnon and Mike Roth, which highlights Diophantine properties of Seshadri constants.