### The dynamical shape of a complex polynomial

- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 8, 2009 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Laura DeMarco – Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago

A classification of the dynamics of polynomials in one complex variable has remained elusive, even when considering only the simpler "structurally stable" polynomials. In this talk, I will describe the basics of polynomial iteration, leading up to recent results in the direction of a complete classification. In particular, I will describe a (singular) metric on the complex plane induced by the iteration of a polynomial. I will explain how this geometric structure relates to topological conjugacy classes within the moduli space of polynomials.