La cuarta escuela tendrá lugar en la Facultad de Ciencia y Tecnología de la Universidad de La Rioja, Logroño, durante durante los días 6 al 9 de mayo de 2024.
La escuela constará de tres minicursos cursos y varias sesiones de trabajo.
Cursos:
- Título: Orthogonality and bispectrality.
Profesor: Antonio J. Durán.
Abstract: In these lectures, we will consider two important extensions of the classical and classical discrete orthogonal polynomials. On the one hand, Krall or bispectral polynomials which, besides the orthogonality, are also common eigenfunctions of higher-order differential or difference operators; on the other hand, exceptional polynomials which have recently appeared in connection with quantum mechanics models associated to certain rational perturbations of the classical potentials. We also explore the relationship between both extensions and how they can be used to expand the Askey tableau. - Título: Orthogonal polynomials and representation theory.
Profesor:
Maarten van Pruijssen.
Abstract: In this course we describe how matrix-valued polynomials arise naturally in the context of multiplicity free representation theory of compact groups. We will see how the relation to group representations gives rise to explicit results for the matrix-valued polynomials; orthogonality, recursion relations, differential operators, etc. In the scalar-case this amounts to the identification of the zonal spherical functions with the Jacobi polynomials in rank one and with Heckman-Opdam polynomials in general and we will see how this generalizes to the matrix case. The emphasis is on specific examples and the required representation theory will be recalled. - Título: An introduction to matrix valued orthogonal polynomials.
Profesor: Pablo Roman.
Abstract: The goal of this course is to present an introduction to the theory of matrix valued orthogonal polynomials. The theory was initiated by Krein in the 1940s and has connections with a broad range of branches of mathematics, such as harmonic analysis, approximation theory, spectral theory, mathematical physics, etc. The course aims at developing an understanding of the basic notions of matrix orthogonality and the main structural and analytic properties of matrix orthogonal polynomials. There will be emphasis on the study of matrix valued differential and difference operators having the polynomials as eigenfunctions. The Riemann-Hilbert formulation for matrix valued orthogonal polynomials will be discussed. The theoretical concepts will be illustrated with applications to integrable systems.
La apertura del curso tendrá lugar el lunes 9 de mayo a las 9:00 horas y la clausura el jueves 9 a las 18:00.
Horario de las sesiones:
|
Lunes |
Martes |
Miércoles |
Jueves |
|
Durán 9:15-11:15 |
Durán 9:15-11:15 |
Durán 9:15-11:15 |
Durán 9:15-11:15 |
|
Coffe-Break 11:15-11:45 |
Coffe-Break 11:15-11:45 |
Coffe-Break 11:15-11:45 |
Coffe-Break 11:15-11:45 |
|
Roman 11:45-13:45 |
Roman 11:45-13:45 |
Roman 11:45-13:45 |
Roman 11:45-13:45 |
|
Lunch 14:00-16:00 |
Lunch 14:00-16:00 |
Lunch 14:00-16:00 |
Lunch 14:00-16:00 |
|
van Pruijssen 16:00-18:00 |
van Pruijssen 16:00-18:00 |
van Pruijssen 16:00-18:00 |
van Pruijssen 16:00-18:00 |
Organización: La escuela está organizada por el Prof. Óscar Ciaurri (director). El comité local está constituido por Óscar Ciaurri, Alberto Arenas Gómez y Edgar Labarga Varona. La web ha sido diseñada por el Prof. Renato Alvarez-Nodarse.
