Date:	Tue, April 26, 2016
Time:	14:15
Place:	Research I Seminar Room

Abstract: Post-critically finite rational maps can be classified by finite graphs called Hubbard trees. In the spirit of transferring polynomial tools to the transcendental world, I will talk about extending this to the transcendental case, in the setting of post-singularly finite entire functions. The first part of this endavour is showing that singular values are landing points of dynamic rays. Schleicher and Zimmer proved this in 2003 for post-singularly finite exponential maps, but their techniques work in much greater generality. I will present several ideas on how to generalize their statement, with the final goal of covering all post-singularly bounded maps. This is very much work in progress. Once that is settled, the challenge is to construct Hubbard trees from that. It turns out that the definition ought to be adapted slightly, but there we have an approach towards as well; this can also be discussed if time permits.