Title: Arithmetic questions about iterates of quadratic polynomials.

Abstract: In the classical study of holomorphic dynamics, systems defined by iteration of quadratic polynomials received much attention. Many interesting and non-trivial number-theoretic questions arise when one considers similar dynamical systems defined over a global field (Q, say), instead of C. Drawing on the arithmetic theory of elliptic curves as motivation, we'll survey recent results in the arithmetic of (quadratic) dynamical systems.