Dynamics Seminar

Brennan Bell

(Jacobs University)

"Renormalization in complex dynamics: "Crossed" renormalization of quadratic polynomials"


Date: Tue, February 23, 2010
Time: 14:00
Place: Research I Seminar Room

Abstract: Douady and Hubbard introduced "simple" renormalization in the 1980's. Fields medalist McMullen studied renormalization theory within Complex Dynamics, and came across another type of renormalization, called "crossed" renormalization. In response to McMullen's request for a description of this new kind of renormalization, Johannes Riedl and Dierk Schleicher studied the locus of crossed renormalization, and give a complete description of it in their paper "On Crossed Renormalization of Quadratic Polynomials." The purpose of this talk is to present (some) of the results in their paper: in particular, the several types of renormalization in complex dynamics, and the main result of the paper, "The Locus of Crossed Renormalizations," are studied. If time permits, the relationship described in the paper between crossed renormalization and internal addresses will be covered.