About

Description. The goal of the school is to provide participants with knowledge, methods and tools related to the field of orthogonal polynomials and special functions, as well as different applications. The 2024 summer school is part of a series of OPSFA-summer school. In the objectives of this Summer School, there is not only the presentation of the classical aspects of orthogonal polynomials and special functions, but also new operational techniques and new approaches related to the unconventional aspects for this field will also be discussed, such as for example the study of orthogonal polynomials in the context of fractional calculus both with the standard method and through the techniques and related formalism of translation operators, the extension of special functions to the complex field and also the use of Sobolev spaces for the definitions of orthogonal polynomials via a different inner product. 

This School will give you the opportunity to discuss mathematics and to participate in modern research in the OPSFA. The summer school topics have relationships with topics in the standard curriculum of a degree course in mathematics and/or physics or some special program of engineering, such as differential equations and linear algebra, mathematical analysis, real and complex analysis, group theory and operator theory, numerical methods and approximation theory. We expect you to be familiar with these topics.

Learning outcomes. After this course the participant should be familiar with hypergeometric functions of several variables and will understand its relation to harmonic analysis. The participant will understand the role of orthogonal polynomials and special functions in quadrature rules and Krylov subspace methods. The participant will know what modular functions are, and understand their relation to group theory and complex analysis. The participant will understand the role of orthogonal polynomials and quantum information, in particular in relation to perfect state transfer. The participant will be familiar with the basic results on matrix orthogonal polynomials, and their relation to matrix differential operators.

This course is designed for. This summer school is dedicated primarily to doctoral or post-doctoral students working in the field of special functions and orthogonal polynomials as well as in fields related to this topic, such as approximation theory or numerical analysis. Nonetheless, considering the multiple applications that special functions and orthogonal polynomials allow, the school can also be used by students or young researchers who in other research fields use the methods and tools of special functions and orthogonal polynomials.

Admission requirements. Participants are required to have solid experience in basic mathematics and in particular in mathematical analysis and numerical analysis; furthermore, participants must hold consolidated knowledge of the topics related to ordinary and partial differential equations, operational techniques, numerical methods, as well as the comprehension of the basics of special functions and orthogonal polynomials.