##### Speaker

Dr. Scott Kaschner, Butler University

##### Title

Complex Dynamics: From One to Several Variables

##### Physical Location

Allen Hall 411

**Abstract:** I will discuss the standard tools used in the iteration of rational maps of one complex variable and give a brief history of the field. Then I will illustrate these tools' use in a project about maps, f, given as the sum of a degree n power map and a fixed degree d polynomial. This project explores the geometric limit as n approaches infinity of the set of points that remain bounded under iteration by f. A brief background of the dynamics for rational maps of several complex variables will follow, detailing the shortcomings of strategies from one variable and the new strategies required. I will illustrate these with a project about various types of postcritically finite maps of P^k and present examples of each type.