Abstract: An inner function is a holomorphic self-map of the unit disk such that for almost every theta in [0,2\pi), the radial limit of F(re^{i\theta}) exists and has absolute value 1. Inner functions have traditionally been studied in terms of their zeros. This approach leads to Beurling's invariant subspace theorem, which is one of the cornerstones of modern function theory. One can also study inner functions in terms of their critical points. In this talk, we will take a third route and study inner functions from the perspective of their critical values.
