6 problems

Let $\mathcal{F}_a$ be the correspondence in the family described above, $\mathcal{M}$ the Mandelbrot set, and $\mathcal{M}_{\Gamma}$ the modular Mandelbrot set, namely the set of…

Let $\mathcal{F}_b:=J_b\circ\operatorname{Cov}_0^Q$ be the family associated to a degree $d+1$ polynomial $Q$ with two critical points, one of which is simple, and an involution…

Let $d$ be a degree, let $P$ be a polynomial of degree $d$ with connected Julia set, let $Q$ be a polynomial of degree $d+1$, and let $J$ be an involution. A Hecke-group mating con…

Bullett's conjecture. For all parameters $a$ in the modular Mandelbrot set, the correspondence $F_a$ is a mating between a quadratic polynomial with connected Julia set and…

An expanding Thurston map is a branched covering of the sphere whose dynamics admit a suitable expanding metric, and an anti-mating is a function associated with a pullback curve w…

Let $P$ and $Q$ be quadratic polynomials with locally connected Julia sets, and let $p$ and $q$ denote their corresponding parameters in the Mandelbrot set. The quadratic mating co…