Harmonic Analysis was originally devoted to the study of Fourier series. Their applications are ubiquitous in Physics, Electrical Engineering, and many branches of Computing, but also behind much of modern-day Pure Mathematics, for example in Differential Equations or Number Theory. Today, we know many other ways of expanding functions, for example different types of wavelets, Gabor frames, or even systems of analytic functions. Such function representations can be very efficient tools to compress, store data and reconstruct data, and indeed much of the drive for the development of these new function bases came from electrical engineering and from signal processing. But the development of wavelet and other representations has also had a profound impact on classical analysis. In recent years, a number longstanding open problems in Analysis could be solved, because wavelet and other expansions offered efficient ways to "discretize" a problem. The group is interested in both the theoretical and applied aspects of such function bases expansions, and how to make use of them for constructing fast algorithms for partial differential equations, integral equations and inverse problem