For the Sciences Festival in Paris, I gave a lecture in Jussieu on Saturday, November 21st. The title was “La conjecture (résolue) de Poincaré : flots géométriques et applications”. I described the curve shortening process and its application to images denoising. After a description of the classification of orientable and closed surfaces, I stated the Poincaré conjecture. I then attempted an intuitive definition of the Ricci curvature and alluded to Hamilton’s Ricci flow.