Mathematics Colloquium: Thurston sets: bagels, teapots, and rings of fire

Speaker:  Kathryn Lindsey, Boston College

Title:  Thurston sets: bagels, teapots, and rings of fire

Abstract :  One of the last papers by the late W. Thurston contained a stunningly beautiful, complex, and mysterious image -- the shape has been described as a "bagel," a "ring of fire," or, more prosaically, a "Thurston set."  The image depicts a subset of the complex plane consisting of all the Galois conjugates of all the growth rates of critically periodic, real quadratic polynomials.  As I will explain, this set is an analogue of the celebrated "Mandelbrot set" for a family of iterated function systems; it has interesting connections to multiple active fields of research.  The surprise revealed by Thurston's image is that this set has a great deal of geometric/topological structure.  Over the past few years, my collaborators (in particular, Harrison Bray, Diana Davis, Giulio Tiozzo and Chenxi Wu) and I have been working to understand the structure of this set and what it tells us about the growth rates of polynomial maps.  I will discuss some of our discoveries and also questions that remain mysterious.

Time:  Friday, September 15, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person