Common preperiodic points for quadratic polynomials

Laura DeMarco, Holly Krieger, Hexi Ye

Let $f_c(z)=z^2+c$ for $c\in \mathbb{C}$. We show there exists a uniform bound on the number of points in ${\mathbb{P}}^1(\mathbb{C})$ that can be preperiodic for both $f_{c_1}$ a…