Alan Sola: Derivatives of rational inner functions: geometry of singularities and integrability at the boundary

Rational inner functions are ratios of polynomials of several complex
variables that are analytic in the unit polydisk and attain modulus 1 at every
point on the unit polytorus. Unlike in one variable, such functions may have
essential singularities at boundary points due to numerator and denominator
vanishing simultaneously without sharing a common factor. I will report on
recent joint work with K. Bickel and J.E. Pascoe on RIFs and their boundary
singularities, and how the precise nature of these singularities determine
integrability and regularity properties of derivatives of RIFs and related
rational functions.