Topology of quadrature domains

We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.Comment: 37 pages, 11 figures in J. Amer. Math. Soc., Published electronically: May 11, 201

Planar Orthogonal Polynomials As Type II Multiple Orthogonal Polynomials

We show that the planar orthogonal polynomials with $l$ logarithmic singularities in the potential are the multiple orthogonal polynomials (Hermite-Pad\'e polynomials) of Type II with $l$ measures. We also find the ratio between the determinant of the moment matrix corresponding to the multiple orthogonal polynomials and the determinant of the moment matrix from the original planar measure