"Classical questions in Diophantine Geometry and their relation to Algebraic Dynamical Systems on the Riemann Sphere"
Abstract: We will explain how the study of preperiodic points for algebraic dynamical systems puts into perpective many open problems in diophantine geometry (e.g. Lehmer conjecture, the abc conjecture, effective bounds for rational points). We will introduce the main tools: canonical height, equidistribution of sequences of small points. Function field analogues will also be mentioned.