Colloquium: "Shapes of Julia Sets"

Kathryn Lindsey, University of Chicago

Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded.  William Thurston asked "What are the possible shapes of polynomial Julia sets?"  For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name?  It turns out the answer to all of these is "yes!"  I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.  
 

Tea @ 3:45 in Cupples I, Room 200

Host: Renato Feres