13. Understanding properties of extremal Blaschke products
Understanding properties of extremal Blaschke products $B_A$ associated with a matrix $A$ (I propose to call them Crouzeix’s Blaschke products):Specifically designed numericall experiments may help to investigate these problems.

Problem 13.3.
[E. Wegert] What are geometric properties of the subclasses $A\in\mathbb{C}^{d\times d}$ with $\mathrm{deg}\,B_A=k$, $k=0,\ldots,d$? 
Problem 13.4.
[E. Wegert] Are there relations between the Blaschke product $b$ generating a compression $S_b$ of the shift (Pamela Gorkin’s talk) and its (extremal) Crouzeix Blaschke product $B$?
Cite this as: AimPL: Crouzeix's conjecture, available at http://aimpl.org/crouzeix.