This is an ongoing project with Kathryn Lindsey and Giulio Tiozzo. The dynamics of post critically finite quadratic maps can be encoded via maps on their Hubbard trees, and the entropy of these map, called the core entropy, has been extensively studied. The goal of the project is to generalize Tiozzo's prior result on the continuity of core entropy, by studying the distribution of the Galois conjugates of its exponent. I will discuss some preliminary results when the post critical orbit is periodic. Speaker(s): Chenxi Wu (UWisconsin)