I will discuss a class of matrix valued orthogonal polynomials (MVOP) that arise from random tilings of a hexagon with doubly periodic weightings.The matrix valued orthogonality is closely connected to scalar orthogonality on a Harnack curve, which is an algebraic curve with very special properties. The zeros of the scalar orthogonal functions distributed themselves along a contour on the Harnack curve. I will explain that the weak limit of the normalized zero counting measures is an equilibrium measure for a bipolar Green’s energy in an external field. This measure is a main ingredient for the Deift/Zhou steepest descent analysis of the Riemann-Hilbert problem.
The talk will be followed by a Junior Reading Group on Orthogonal Polynomials and Random Matrices (from 3.15 pm to 4.15 pm)
