Title: A Geometric Approach to Runge's theorem

Abstract: We will recall Runge's theorem on approximation of analytic functions (in one complex variable) by polynomials, and remark how a lack of a global understanding of the polynomial approximant limits potential applications of this theorem in complex dynamics. We will discuss a different approach to this classical result which gives a fuller understanding of the polynomial approximants, and discuss potential applications. This talk is based on joint work with Chris Bishop.