Abstract: I will discuss some geometric aspects of my recent work with Kelly Bickel and Alan Sola concerning rational inner functions on the bidisk. A rational inner function on the bidisk is a bounded rational map defined on the bidisk such that it is unimodular almost everywhere on the torus. I will discuss how the geometry of the level sets relates to membership of the partial derivatives in Hardy spaces. Surprisingly, we obtain that increased non-tangential regularity at a singularity decreases the range of Hardy spaces to which the partial derivatives can belong.
Host: John McCarthy