François Labourie

François Labourie (* December 15, 1960 in Rouen ) is a French mathematician.

Labourie went to Rouen to school and studied 1980-1985 at the Ecole Normale Superieure. In 1987 he received his doctorate in Mikhail Gromov (topology géométrie et des surfaces localement convexes ). From 1985 he was a researcher of the CNRS at the Ecole Polytechnique, where he also was an assistant professor from 1991 to 2001. In 1993 he qualified as a professor at Albert Fathi and Robert Rooms at the University of Paris-Sud, where he has been a professor since 1994.

Labourie deals with differential geometry, where he studied, among other convex hypersurfaces, pseudoholomorphic curves and Anosov flows, operations of groups ( bars ) on manifolds. Here he built at great length on the ideas of Gromov. He also made important contributions to the generalization of Teichmüller theory to higher dimensions using projective structures (double standards). With Yves Benoist and Patrick Foulon he solved a long open question about Anosov flows on compact contact manifolds.

In 1992 he was awarded the EMS price and Carrière 1993 Prize of the French Academy of Sciences. In 1998 he was invited speaker at the ICM in Berlin ( Large group actions on manifolds ). In 2006, he gave a keynote lecture at the annual meeting of the German Mathematical Society ( Higher Thurston Theory). Since 1997 he is member of the Institut Universitaire de France.

Writings (selection )

• With Y. Benoist: Sur les difféomorphismes d' Anosov affine à feuilletages stable et instable différentiables. Invent. Math 111 (1993), no 2, 285-308.
• Un lemme de Morse pour les surfaces convexes. Invent. Math 141 (2000), no 2, 239-297.
• With M. Burger, A. Iozzi, A. Wien Hard: Maximum representations of surface groups: symplectic Anosov structures. Pure Appl. Math Q. 1 (2005 ), no 3, Special Issue: In memory of Armand Borel. Part 2, 543-590.
• Anosov flows, surface groups and curves in projective space. Invent. Math 165 (2006), no 1, 51-114.
• Cross ratios, surface groups, PSL (n, R) and diffeomorphisms of the circle. Publ Math Inst Hautes Études Sci. No. 106 (2007), 139-213.
• With W. Goldman, G. Margulis: Proper affine actions and geodesic flows of hyperbolic surfaces. Ann. of Math ( 2) 170 (2009 ), no 3, 1051-1083.