A research progression from weighted shifts

After a gentle introduction to Hilbert space operator theory, we will begin with the humble weighted shift.  We'll follow a trail of recent results, including a new property for such shifts stronger than subnormality, a new and rich class of examples of weighted shifts, and some directions suggested by the class:  an improved understanding of the role of Bernstein functions and the introduction of signed measures to extend the role of measures in the classical theory.  The talk is based on joint work with Chafiq Benhida (University of Lille) and Raul Curto (University of Iowa).