Arithmetic Groups

Let $f = \sum a_n x^n \in \mathbb Q[x]$ be a power series which is also a meromorphic function in some neighborhood of the origin. The subject of the talk will be how certain conditions on $f(x)$ as a meromorphic function actually guarantee that $f(x)$ is an algebraic function of $x$. We shall begin by describing a common theme which runs through many such arguments. We then shall discuss a number of examples of such theorems (including a new such result).