6 problems

The unilateral frame number conjecture.

The $C_{\theta}$-real matrix representation conjecture. If $M$ is a complex symmetric matrix and is unitarily equivalent to a TTO, then there exist an inner function $u$ and a…

Let $I$ be an inner function, let $K_I^2$ denote the corresponding model space, and let a bounded symbol of a truncated Toeplitz operator mean a symbol in $L^\infty(\mathbb{T})$ re…

Spherical-boundary conjecture. In the model spaces $\mathbb{M}(\kappa)$, every isoperimetric region is bounded by a spherical surface $\mathcal{S}_\lambda(p)$.

One-component characterization conjecture. The equivalent conditions of Theorem 3 are fulfilled if and only if $\theta$ is one-component.

Sarason's quasisymbol conjecture. Every bounded truncated Toeplitz operator $A$ coincides with $A_\mu$ for some $\mu\in\mathcal C_2(\theta)$. Moreover, nonnegative bounded truncate…