Conferenciante: Ana Foulquie (Universidade de Aveiro)
Día:9 de febrero
Lugar: Seminario Física Teórica ,2ª Planta
Título: Riemann-Hilbert problems in the theory of matrix orthogonal polynomials
Abstract: In this talk we present a Riemann-Hilbert problem for matrix orthogonal polynomials in the real line. Taking into account this formulation and for measures that satisfy differential equations of Pearson type we obtain, for the coefficients of the recurrence relation of such polynomials non Abelian versions discrete equations of Painlevé I and alternate Painleve I types.
We also determine, for generalized matrix Hermite polynomials, the equations that the coefficients of the three term recurrence relation satisfy. Also, we present structure equations as well as a matrix eigenvalue problem associated with this family.
Working together with Amílcar Branquinho (University of Coimbra) and Manuel Mañas (Universidad Complutense de Madrid).