1 July - 19 December 1997

**Organisers**:JP Keating (*Bristol*), DE Khmelnitskii (*Cambridge*), IV Lerner (*Birmingham*), P Sarnak (*Princeton*)

The quantum properties of disordered systems have been the focus of considerable attention in many branches of physics, principally nuclear and condensed matter physics. Recently it has been recognised that many of the same phenomena occur in classically chaotic systems as well. Even more surprisingly, there are also strong similarities with the results from number theory concerning, for example, correlations between the zeros of L-functions (eg the Riemann-zeta function). In the past few years an extremely stimulating and productive cross-fertilization between these fields has developed. The aim of the programme is to accelerate the already significant rate of progress on some of the important common problems which occur, in different guises, in each area. The main topics are expected to include localization, fluctuation statistics of spectra and eigenfunctions, random matrix theory, trace formulae, and supersymmetric methods. There will be a particular emphasis on applications to mesoscopic quantum systems.