3 problems

Let $H^2(\mathbb{D}^2)$ be the Hardy space on the bidisk, and let $f$ be a polynomial in this space with no zeros in the closed bidisk. For each multidegree, an optimal polynomial…

Let $\Theta$ be a $d\times d$ matrix-valued inner function on the bidisk, and let $S_{z_1}$ denote the associated compressed shift operator. Write $\deg_1\Theta$ and…

Unbounded-face conjecture. Every $\gamma=(g_1,g_2)$ where both $g_i$'s are hyperbolic admits a Dirichlet domain with more than two faces.