Algebraic Dynamics Seminar: Marked cycle curves for quadratic polynomials and rational maps

We consider the algebraic curves obtained by marking a cycle of fixed period p in the space of quadratic polynomials. For each period, we produce a cell decomposition, whose combinatorics is closely related to the combinatorics of primitive components in the Mandelbrot set. This opens up many questions about their combinatorial and geometric structure. We also consider similar curves for the space of quadratic rational maps with a critical 2-cycle.  Joint work with Caroline Davis, Malavika Mukundan, and Danny Stoll.