Heights are an important component of the number theorist's toolbox. This presentation will describe the basic elements of heights, and how they play a role in many major areas of number theory; ranging from elliptic curves to dynamical systems. The canonical height is a particularly important tool in arithmetic dynamics. In this talk, we will discuss recent developments in the area of canonical heights, and explain an extension to generalized iteration. We will conclude with an open conjecture and discuss how heights may contribute to its solution.
Canonical Heights in Generalized Iterations