In this talk, we will introduce the moduli space \(\mathcal{M}_2\) of rational functions of degree 2, and study the curve \(Per_1(1)\subset\mathcal{M}_2\) of conjugacy classes of quadratic rational maps having a parabolic fixed point with multiplier equal to 1. We can define its Mandelbrot set \(M_1\) to be the connectedness locus of Julia sets in this family. Milnor conjectured that this set is homeomorphic to the Mandelbrot set described in the previous two talks, which has been shown by Petersen & Roesch.

For notes of the talks of this study group, click here.