6 problems

Let $H^{\alpha}$ be the Hardy space associated with a continuous rotationally symmetric norm $\alpha$, let $B$ be a finite Blaschke factor of degree $n$, and let…

Suppose $\rho$ is a tree monodromy representation giving rise to Shabat–Blaschke products of degree $n$ with exactly two critical values in $\mathbb{D}$. For each fixed…

Parabolic-curve accumulation conjecture. Parabolic curves accumulate on the unit circle at isolated points and tangentially to it. Moreover, if a parabolic curve accumulates on a p…

Extended-tongue structure conjecture. The connected components of $ET_\tau$ are disjoint. The boundary of every connected component consists of two disjoint connected components: a…

Refined Zhu's conjecture. The number of minimal reducing subspaces of $T_B$ equals the number of connected components of this Riemann surface for every finite Blaschke product $B$.…

Let $\phi$ be a Blaschke product of finite order, and let $M_\phi$ denote multiplication by $\phi$ on the Bergman space $L_a^2$. Consider the Riemann surface of the multivalued map…