*Programme leaders: G. van Dijk, T.H. Koornwinder*

Central research themes are:

(1) analysis on Lie groups, semisimple symmetric spaces and quantum groups

(2) special functions associated with root systems and their interpretation on the above-mentioned structures

(3) analysis, asymptotics, approximation theoretic properties and algorithmic aspects of special functions and orthogonal polynomials in one variable (including the cases of orthogonal rational functions and orthogonality in a Sobolev space)

(4) approximation problems with relation to potential theory

(5) analysis in several complex variables

(6) wavelets

(7) analysis aspects of modern mathematical physics, in particular the classification of integrable evolution equations.

This programme unites a number of themes which are mutually connected and have a stimulating influence on each other. Some themes have a quite algebraic setting, while others belong to classical analysis. Theme (2) dealing with Heckman-Opdam hypergeometric functions and q-analogues like Macdonald polynomials is a highlight of the programme. A new line within theme (1) is the study of canonical representations for Hermitian and para-Hermitian symmetric spaces, and its relation with Berezin quantization. A new interesting development within theme (3) is the involvement with the production of the new version of the famous ``Handbook of Mathematical Functions'' (Abramowitz & Stegun). This new edition will become available as an interactive database on the internet.