Date:	Tue, February 25, 2014
Time:	14:15
Place:	Research I Seminar Room

Abstract: The purpose of this talk is to give some necessary background for the second talk, on real laminations of Julia sets of polynomials. In the first part of the talk, we will discuss cross-cuts and prime ends, in order to state Caratheodory's theorem on local connectivity. The focus of the talk will actually be on a theorem that, for connected polynomial Julia sets, rational dynamical rays land. We will mention, without proof, the Schwarz-Pick lemma. It is a crucial tool in the proof of this theorem. The analogous result, that every repelling or parabolic periodic point is the landing point of at least one ray, is proved in this section of Milnor, but requires more time than we have, so we will not be discussing that. In particular, we will be following closely with chapters 17 and 18 of Milnor's Complex Dynamics in One Variable.