Bourbaki goes to Luxembourg (garden)

On march 15th, 2009, I gave the Bourbaki lecture on “the differentiable sphere theorem”. As a protest against the government policy, the beginning of the lecture has been given on the bandstand of Jardin du Luxembourg. After ten minutes we had to leave when the senate police arrived. We then finished the lecture in  the regular room at Institut Henri Poincaré. A video is posted on You Tube.

The power of mathematics, why they still are unavoidable

The magazine La Recherche recently published a special issue (Les Dossiers de La Recherche n°37 trimestriel novembre 2009). An improved  version of a previous paper appeared in this volume. It is entitled  “Comment on est venu à bout de la conjecture de Poincaré” and contains a wide-audience description of Perelman’s works on Hamilton’s Ricci flow leading to  the proof of Poincaré’s Conjecture. A previous version also published in La Recherche is available here.

Collapsing irreducible 3-manifolds with nontrivial fundamental group

This is a joint work with Laurent Bessières, Michel Boileau, Sylvain Maillot and Joan Porti. Let M be a closed, orientable, irreducible, non-simply connected 3-manifold.We prove that if M admits a sequence of Riemannian metrics which volume-collapses and whose sectional curvature is locally controlled, then M is a graph manifold. This is the last step in Perelman’s proof of Thurston’s Geometrisation Conjecture.

The reference is:

L. Bessières, G. Besson, M. Boileau, S. Maillot and J. Porti Collapsing irreducible 3-manifolds with nontrivial fundamental group Invent math (2010) 179: 435–460.

Sciences Festival in Paris

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.