April 11, 2023

Workshop on Integrable Systems and Orthogonal Polynomials – Numerical and Analytical Perspectives

Dates:

11 to 15 April 2023

Organisers:

Prof. Kerstin Jordaan (UNISA) and Prof. Peter Clarkson (University of Kent)

Description:

This workshop will focus on the relationship between integrable systems, in particular the Painleve equations and discrete Painleve equations, and orthogonal polynomials from both numerical and analytical perspectives. The Painleve equations, continuous and discrete, are nonlinear analogs of the classical special functions and form the core of modern special function theory. In recent years various interesting connections between Painleve equations and orthogonal polynomials have been studied. For example, rational solutions and special function solutions of Painlevé equations have a close relationship with orthogonal polynomials. The relationship between orthogonal polynomials and Painleve equations has interesting applications, for example to random matrices. From a numerical perspective, reliable and efficient evaluation of solutions of Painlevé equations poses significant challenges, and several approaches have been proposed in the literature, including initial value and boundary value methods in the complex plane and numerical calculation based on the Riemann-Hilbert formulation. Presentations will include survey type lectures on important developments in the area as well as lectures on recent results and open problems.

Target Audience:

Researchers, Postdoctoral Fellows, PhD and Master’s students. Spaces are limited.

To apply please click here

Contacts:

Closing Date for Applications: 15 December 2022

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