This workshop will focus on the recent developments in the study of L-functions. The driving themes are: vanishing of L-functions, zero-free regions, size of L-functions, moments. There was a large number of new and exciting results on those subjects in the last few years, and there are very tentalizing questions which are just at the limit of the current techniques. A crucial notion which has emerged over the last decade is that L-function should be studies in families, a notion which is also at the heart of the work of Katz and Sarnak, which explores the mysterious connections between random matrix theory and properties of L-functions, and which has been an important source of inspiration for the recent work on L-functions. The goals of this workshop are to bring together the leading researchers in the world, and to introduce junior mathematicians to the current research on L-functions.

The workshop will include three series of lectures by P. Michel (Montpellier), K. Murty (Toronto) and K. Soundararajan (Michigan), surveying the key ideas and recent progress on L-functions, and presenting the new directions in the field.