Alan Sola: Singularities of rational inner functions in higher dimensions

Reporting on joint work with K. Bickel and J.E. Pascoe, I will present results concerning the boundary behavior, level sets, and partial derivatives of rational inner functions in the tridisk, and in higher-dimensional polydisks. In contrast to their two-dimensional setting which is relatively well-understood, the geometry of RIFs in three or more variables exhibits many pathologies and surprising properties, some of which will be described in my talk.