Caroline Davis (Indiana University)

A tour of Per_n(0)

In this talk, we survey recent work about the internal structure of the dynamical varieties Per_n(0) in the space of quadratic rational maps, varieties which are defined by marking a n-periodic critical point. We will discuss the structure of these spaces near their punctures as well as define the “mating” of two quadratic polynomials and see what application this has for elucidating global topological information about the varieties, such as connectivity