Analysis Seminar: Polynomials with no zeros on the unit ball

Abstract: There is a large and well-developed theory with numerous applications for polynomials with no zeros on the polydisk (and the equivalent family of polynomials with no zeros on the product of upper half planes).  The other standard model domain, the unit ball in C^n, has virtually no theory for the class of polynomials with no zeros there.  We will review a few things that are known and then discuss recent work about a local description of the zero set of a polynomial with no zeros on the unit ball but with a boundary zero.  I will also discuss a natural open problem discovered along the way that we cannot yet solve.  This is joint work with Alan Sola and James Pascoe.

Host: Alan Chang