Laura DeMarco : The dynamical shape of a complex polynomial

Posted by Emily Dumas , part of the Graduate Student Colloquium.

At

Nov. 20, 2009, 3 p.m.

In

SEO 636

Abstract

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.