A special Millican Colloquium in recognition of Joseph P.S. Kung's retirement from UNT and in celebration of his mathematical career. Note the later than usual starting time.
Abstract: Goncarov Polynomials are the solutions of the classical Goncarov Interpolation Problem, which have been studied extensively by analysts due to their significance in the interpolation theory of smooth and analytic functions. A parking function is a discrete structure lying in the center of combinatorics with relations and applications to geometry, algebra, representation theory, and physics models. In 2000, using linear functionals and the theory of biorthogonal polynomials, Joseph Kung established an important connection: Goncarov Polynomials form a natural basis for working with parking functions. Many enumerative formulas follow from this connection. In this talk we will review Kung's work and then present a recent extension, where the differential operator is replaced with a delta-operator. This leads to a theory of delta-Goncarov polynomials, which describes a version of "parking functions" inside every binomial structure.