Complex Analysis, Dynamics and Geometry Seminar

In this talk, we explore the structural similarities in the connectedness loci of unicritical polynomials of various degrees, and introduce a way to study these similarities. The main result presented in the talk is that postcritically finite unicritical parameters of any degree d can be embedded into the space of PCF unicritical parameters of degree d+1, in a way that is 'consistent' at the level of the Hubbard tree, and the underlying spider. We also discuss consequences to core entropy of PCF unicritical polynomials. We end by considering possible extensions of these embeddings, and further directions to explore. Speaker(s): Malavika Mukundan (U(M))