Abstract
Membranes occur in several domains such as biology, chemical physics, condensed matter and high-energy physics. The interest in membranes has been increasing these last years since the discovery of graphene which is the first genuine two-dimensional material. There are two kinds of membranes: fluid and polymerized. My research is on polymerized phantom membranes which are studied using a nonperturbative renormalization group approach. This allows to investigate the crumpling transition and the flat phase for a D-dimensional membrane embedded in a d-dimensional space.