Blaschke Products, Numerical Ranges & the Zeros of Orthogonal Polynomials by Brian Simanek, Baylor U

Blaschke Products, Numerical Ranges & the Zeros of Orthogonal Polynomials by Brian Simanek, Baylor University,  Class of 1960 Scholar,  November 10, 1:00 – 1:50pm, North Science Building 015, Wachenheim

Abstract: Our main object of interest will be the location of zeros of orthogonal polynomials on the unit circle. After recalling some fundamental results, we will discuss more recent developments that relate these zeros to Blaschke products, numerical ranges of matrices, algebraic curves, and quadrature measures.  Special attention will be paid to the relationship between paraorthogonal polynomials on the unit circle and Poncelet’s Theorem.  Some open problems will be mentioned along the way.  This is based on joint work with Markus Hunziker, Andrei Martinez-Finkelshtein, Taylor Poe, and Barry Simon.