**Title:** Shapes of polynomial Julia sets

**Speaker:** Kathryn Lindsey, University of Chicago

**Date and Time:** Friday, February 10, 2:15-3:15pm

**Place:** Rome 351

**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. W. 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.