Szego Seminar: "Poncelet Ellipses, Finite Blaschke Products, and the Numerical Range"
Nathan Wagner, Washington University in Saint Louis
Abstract: In this talk, we examine a surprising connection between a classical geometric result due to Poncelet, finite Blaschke products, and the numerical range of certain finite-dimensional operators. In particular, in certain cases the numerical range of the compression of the shift corresponding to a finite Blaschke product is an elliptical disk. This leads to a proof of a nice geometrical property of degree-4 Blaschke products that are compositions.
Host: Christopher Felder