- President, European Research Council
- Former Director, Institut des Hautes Études Scientifiques (IHÉS) from 1994 till 2013.
- A mathematician by training, specialized in differential geometry and mathematical aspects of theoretical physics
- Fellow of the Centre National de la Recherche Scientifique (CNRS)
- Held a Professor position at École polytechnique from 1986 to 2012
- President of the Société Mathématique de France, 1990 to 1992
- President of the European Mathematical Society, 1995 to 1998
- Former member of the Board of the EuroScience organisation (2002-2006)
- Served on EuroScience Open Forum (ESOF) committees, 2004 to 2013.
- Received the Prix Paul Langevin in 1987 and the Prix du Rayonnement Français in Mathematical Sciences and Physics from the Académie des Sciences de Paris in 1997.
- He is a foreign member of the Royal Spanish Academy of Sciences.
- Elected honorary member of the London Mathematical Society, 2005
- Secretary, mathematics section of the Academia Europaea.
- Doctor Honoris Causa of Keio University, Japan, 2008
- Doctor Honoris Causa of Nankai University, China, 2011