Title of the course: Crash Course on Arithmetic Dynamics
Instructor: Prof. Turgay Bayraktar
Institution: Sabancı University
Dates: 14-20 September 2026
Prerequisites: 3xx level Complex Analysis and Algebra
Level: Graduate, advanced undergraduate
Abstract: Arithmetic dynamics studies the interaction between number theory and dynamical systems through the iteration of algebraic maps. In this short introductory course, we explore how tools from complex dynamics, potential theory, and arithmetic geometry combine to describe the distribution of algebraic points and the behavior of canonical height functions. Starting from classical height functions and equidistribution results such as Bilu’s theorem, we develop the basic framework of dynamical systems on the Riemann sphere and their associated potential theory. We then introduce canonical heights and equidistribution phenomena arising from iterated rational maps, highlighting both complex and non-archimedean aspects. The course provides an accessible overview of key ideas including Julia sets, escape-rate functions, capacity and equilibrium measures, and the role of Berkovich spaces in p-adic dynamics.The goal is to give participants a conceptual roadmap of modern arithmetic dynamics, emphasizing fundamental examples and guiding principles rather than technical completeness. The course assumes basic knowledge of complex analysis and algebra but is otherwise self-contained.
Language: English