Learning outcomes

By the conclusion of the OPSFA Summer School (OPSF-S11), participants will have gained a solid understanding of a variety of advanced topics at the forefront of current research in orthogonal polynomials and special functions. These include:

1. Asymptotic methods for orthogonal polynomials, with emphasis on techniques used to analyze their behavior in various limiting regimes, as well as generalized Padé approximants, including their construction, convergence properties, and relevance in approximation theory and complex analysis.
2. Interrelations between orthogonal polynomials and other key areas such as sparse interpolation, exponential analysis, and Gaussian quadrature, highlighting both theoretical frameworks and computational applications in Padé approximation and Gaussian integration.
3. Understand the asymptotic behavior of Jacobi polynomials with varying parameters, learning basic tools from potential theory and Riemann-Hilbert methods and applying these techniques to analyze random tilings.
4. Orthogonal polynomials in several variables, including their algebraic structure, differential properties, and role in multivariate approximation.
5. Diagrammatic methods and harmonic analysis techniques, which provide powerful tools for understanding the algebraic and analytic structure of orthogonal polynomials in both classical and modern contexts.

Level of participants

• Master’s students.
• PhD students.
• Post-doc researchers.
• Early-career researchers.

This course is designed for

The OPSFA Summer School (OPSF-S11) is primarily intended for doctoral and postdoctoral students specializing in special functions and orthogonal polynomials, as well as related areas such as approximation theory and numerical analysis. However, given the broad range of applications of special functions and orthogonal polynomials, the OPSFA Summer School (OPSF-S11) is also open to students and early-career researchers from other disciplines who employ these methods and tools in their work. Master’s students nearing the completion of their degrees, or those considering pursuing a PhD, are also welcome to attend, along with young researchers already engaged in academic research.

Mode of study

The OPSFA Summer School (OPSF-S11) will take place at the Escuela Internacional of the University of Alcalá (EIVI), in Alcalá de Henares (Spain). All courses will be conducted in English.

Certificate

Participants who actively engage in the OPSFA Summer School (OPSF-S11) and successfully complete all assignments will receive a certificate of attendance, which will indicate the number of hours attended.

Course organization

The OPSFA Summer School (OPSF-S11) features five lecture series delivered by leading experts in the field. These sessions will be supported by tutorials, exercise classes, and potentially additional talks. Active engagement is expected, and participants are encouraged to interact both with one another and with the lecturers and organizers throughout the event.