Seung-Yeop Lee: Sharpness of the connectivity bound for quadrature domains

Abstract:

Given the order of quadrature domains, the maximal connectivity of the domains were found (http://arxiv.org/abs/1307.0487).  In this talk, we show that the bound is sharp.  The maximal quadrature domains are constructed by (maximally) packing the image of certain univalent polynomials (whose existence was shown by Suffridge).  The result has an application in the maximal number of roots for harmonic polynomials.  This is a joint work with Nikolai Makarov.