Arno Kuijlaars
(Katholieke Universiteit Leuven)
Multiple orthogonal polynomials and the asymptotic analysis of 3x3 matrix valued Riemann-Hilbert problems
Multiple orthogonal polynomials are an extension of orthogonal polynomials in which the orthogonality is distributed over a number of measures. They can be characterized by means of a Riemann-Hilbert problem, which in the case of two measures is 3x3 matrix valued. In the talk I give an overview of some of the algebraic properties and I will cover an example where the asymptotic analysis of a 3x3 Riemann-Hilbert problem
can be carried out with the steepest descent method
of Deift and Zhou.