Rigidity and uniformity in algebraic dynamics

The periodic orbits and their structure are fundamental features of a dynamical system. In an algebraic setting, where the system is defined by polynomials, we can use tools from algebraic or arithmetic geometry to study these orbits.  Important examples come from the study of abelian varieties, but already the setting of polynomials of one variable is a challenge. In this talk, I will describe some open questions and recent progress on families of complex and arithmetic dynamical systems.

https://people.math.harvard.edu/~demarco/