Analysis Seminar: "Extreme Points and Saturated Polynomials"

Abstract: Consider the set of holomorphic functions from the polydisk to the right half plane normalized to send 0 to 1.  What are its extreme points?  We will discuss a construction of some rational extreme points in two variables which are built out of polynomials that we dub "saturated."  They are saturated because they have no zeros in the bidisk but as many zeros on the boundary as possible without having infinitely many zeros.  We will also discuss a conjecture related to two variable extreme points and its implications for determinantal representations.

Host: John McCarthy