7 problems

Let $\mathcal H_d$ be the central hyperbolic component in the space of degree-$d$ rational maps. A rational map is geometrically finite if every critical point in its Julia set has…

Let $\nu_t$, $0<t<1$, denote the Lyons conductance measure describing effective conductance in a Galton–Watson tree with equal weights, arising as a self-conformal measure for a no…

Let $\mathbf M$ be the Mandelbrot set of quadratic polynomials, and let $\mathbf M_1$ be the connectedness locus in the family of rational maps with multiplier $1$ at a fixed point…

Let $\mathcal{M}_d^*$ be the multicorn of degree $d$, let $\mathcal{C}_1$ and $\mathcal{C}_2$ be distinct parabolic arcs in $\mathcal{M}_d^*$, and let $\omega$ denote the relevant…

Let $\mathcal{C}$ be a parabolic arc, and let $\operatorname{ind}_{\mathcal{C}}$ denote the function assigning the parabolic fixed-point index along that arc. No universal paraboli…

Let $d$ be the degree of a multicorn, let $\omega$ denote the rotational symmetry used in the parameter space, and let $H_1$ and $H_2$ be hyperbolic components of odd periods $k_1$…

Let $\mathcal{M}_d^*$ denote the degree-$d$ multicorn, and let a parabolic arc of $\mathcal{M}_d^*$ be parametrized by the critical Ecalle height. Non-singularity conjecture. The c…