OPUC and Super Telescoping Formula

Speaker: Mohammad Javad Latifi Jebelli (Dartmouth, Mathematics)

Date: 9/13/23

Abstract: To every measure on the unit circle, S^1, one can associate a sequence of orthogonal polynomials in the variable z=exp(it). For example, if we look at the uniform probability measure on the unit circle the basic Fourier theory suggest that the polynomials 1,z,z^2,… are orthogonal with respect to this background measure. OPUC (orthogonal polynomials on the unit circle) is the theoretical framework for studying such correspondence for arbitrary measures on S^1. In this talk, we go over the basics of OPUC and their applications. We also go over a new one-parameter family of examples for such correspondence, originating from the super telescoping formula.