EVENT DETAILS AND ABSTRACT

Title: Uniformizing Thurston’s bagel
Speaker: Giulio Tiozzo
Speaker Info: University of Toronto
Brief Description:
Special Note: Two hours
Abstract:

Around 2011, W. Thurston plotted a by-now famous fractal set by drawing all Galois conjugates of all entropies of postcritically finite (or superattracting) real quadratic polynomials. The geometry of this so-called “entropy spectrum” has still lot to be explored, and an overarching theme is that this set is the analog of the Mandelbrot set for piecewise linear, rather than holomorphic, maps.

Our goal is to define a uniformizing map for the complement of Thurston's entropy spectrum (informally known as “the bagel”), i.e. a piecewise linear analog of the Riemann map for the Mandelbrot set, by looking at a certain escape rate.

This is work in progress with K. Lindsey.