Throughout much of its history, model theory, which is a branch of mathematical logic, has made significant contributions to the core parts of mathematics. One of these areas of confluence that has been particularly active in recent years is the model theory of difference fields and its interaction with algebraic and arithmetic dynamics. Arithmetic dynamics is concerned with the behaviour of iterates of points on varieties under an algebraic self map. This framework encodes a lot of deep diophantine problems and has become a central area within the broader number theory community. On the other hand, complex dynamics and algebraic geometry also play an important role, and arithmetic dynamics is ultimately an interdisciplinary subject, accessible by a diversity of techniques.

Two significant recent examples of applications of model theory to arithmetic dynamics are the work of Scanlon-Medvedev on polynomial dynamical systems with consequences for Zhang's conjecture and the dynamical Mordell-Lang conjecture, and the work of Chatzidakis-Hrushovski on descent in algebraic dynamics, generalising to higher dimension the theorem of Baker on rational maps of P1 over function fields. In addition to this, Hrushovski's seminal work on the model theory of the Frobenius has had a dramatic impact. For example, his work is an essential part of Amerik's proof of the existence of non-preperiodic Q-points under an infinite-order algebraic dynamical system over a number field.

The aims of this workshop are twofold: first, our main goal is to facilitate interactions between model theorists and arithmetic geometers already working on dynamical questions; and second, to accelerate progress in this subject by attracting attention to the potential applications of model-theoretic techniques.