Date:	Tue, September 16, 2014
Time:	14:15
Place:	Research I Seminar Room

Abstract: We present several open questions in the field of complex dynamics, and we outline approaches towards solving them. The problems deal primarily with the local connectivity of Julia sets of complex polynomials of arbitrary degree. Much is known about the dynamics of polynomials of degree 2, not only because they are unicritical, but also because their moduli space is complex dimension 1. In part motivated by results in the degree 2 case, and partly motivated by new techniques of Inou and Kiwi in to study higher-dimensional parameter spaces of larger families of polynomials using combinatorial Yoccoz puzzles, we seek to classify the obstructions to local connectivity in polynomial Julia sets, which is suggested by Milnor to be known but unproved for the infinitely renormalizable quadratics. Our first results will relate to broadening the existing class of known locally connected polynomial julia sets, before we delve into a deeper study of nontrivial fibers.