Georgia Institute of Technology College of Sciences

This talk concerns two-variable rational inner functions phi with singularities on the two-torus T^2, the notion of contact order (and related quantities), and its various uses. Intuitively, contact order is the rate at which phi’s zero set approaches T^2 along a coordinate direction, but it can also be defined via phi's well-behaved unimodular level sets. Quantities like contact order are important because they encode information about the numerical stability of phi, for example when it belongs to Dirichlet-type spaces and when its partial derivatives belong to Hardy spaces. The unimodular set definition is also useful because it allows one to “see” contact order and in some sense, deduce numerical stability from pictures. This is joint work with James Pascoe and Alan Sola.