The dynamical shape of a complex polynomial

School of Mathematics Colloquium
Thursday, October 8, 2009 - 11:00
1 hour (actually 50 minutes)
Skiles 269
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.