Date:	Tue, November 17, 2015
Time:	14:15
Place:	Research I Seminar Room

Abstract: The core entropy of a postcritically finite point of the Mandelbrot set is the topological entropy of the restriction of the corresponding quadratic polynomial to its Hubbard tree. Recently it was shown by Dudko and Schleicher that this function extends to a continuous function on the whole Mandelbrot set. Shortly afterwards Tiozzo gave another proof, using a different approach.

In his proof, Tiozzo employs ideas of Thurston to convert the problem into a statement about certain directed graphs and then uses an advanced graph theoretical fact to derive the result. The goal of our talk is to present a new proof of that second part which needs only elementary arguments. We will indicate how our approach can also be used to reproof Tiozzo's result about the Hoelder continuity of the core entropy. If time permits, we will also discuss an idea to generalize these results to polynomials of higher degree.

The slides of the talk will be made available at http://fels.tk.