MERCREDI 9 DECEMBRE 2009 11 heures (Attention: heure inhabituelle!) Salle Séminaire 5 Centre de Physique Théorique Marseille-Luminy Gheorghe Nenciu Institut de Mathématiques de l'Academie Roumaine Bucarest Title: Exponentially localized Wannier functions: recent results and open problems. Abstract: Recent results concerning the problem of the existence of exponentially localized Wannier functions are reviewed. In particular the complete solution for the quasi one-dimensional case is given. Some open problems are also discussed.