Francois Labourie

Francois Labourie
Name	Francois Labourie
Birth date	1960
Nationality	French
Fields	Differential geometry; Dynamical systems; Topology
Workplaces	Collège de France; Institut des Hautes Études Scientifiques; École Normale Supérieure; Université Paris-Sud
Alma mater	École Normale Supérieure; Université Paris-Sud
Doctoral advisor	Mikhail Gromov
Known for	Anosov flows; Teichmüller theory; Geodesic laminations; Higher Teichmüller theory

Francois Labourie is a French mathematician known for contributions to differential geometry, dynamical systems, and low-dimensional topology. He has worked on Anosov flows, Teichmüller theory, and geometric structures on manifolds, connecting ideas from hyperbolic geometry, symplectic geometry, and representation theory. Labourie held positions at major French and international institutions and received several prestigious awards for his research.

Early life and education

Labourie was born in France and trained at the École Normale Supérieure, where he studied alongside contemporaries connected to institutions such as the Université Paris-Sud and the Collège de France. He completed doctoral studies under the supervision of Mikhail Gromov at research environments tied to the Institut des Hautes Études Scientifiques and engaged with mathematical circles around the Société Mathématique de France and the Centre National de la Recherche Scientifique. During his formation he interacted with topics shaped by work of figures like William Thurston, Dennis Sullivan, Yakov Sinai, and Stephen Smale.

Academic career and positions

Labourie held faculty or research positions at institutions including the École Normale Supérieure, the Université Paris-Sud, the Institut des Hautes Études Scientifiques, and the Collège de France. He collaborated with researchers at the Mathematical Sciences Research Institute, the Institute for Advanced Study, and research groups affiliated with the CNRS. Labourie's visitorships and seminars connected him with communities at places such as Princeton University, Harvard University, Université Pierre et Marie Curie, and institutes organizing programs by the European Mathematical Society and the American Mathematical Society.

Research contributions and major results

Labourie's work established deep links among Anosov flows, geodesic laminations, and higher-rank Teichmüller theory via the study of discrete subgroups of Lie groups and their deformation spaces. Building on ideas from Mikhail Gromov and William Thurston, he introduced notions that generalized classical Teichmüller space frameworks to representations into groups like PSL(2,R), PSL(n,R), and more general semisimple Lie groups. His contributions include structural results on Hitchin representations related to the work of Nigel Hitchin, positivity concepts connected to Lusztig's theory, and applications to compactification problems studied by Alexander Grothendieck-era geometric approaches.

Labourie proved rigidity and stability properties of Anosov representations, extending concepts from the theory of Anosov diffeomorphisms developed by Anatole Katok and Rufus Bowen, and connected these to dynamics on flag varieties studied in relation to Sullivan-type measures and Margulis invariants. He solved problems concerning the existence of convex projective structures on manifolds influenced by work of Benoist and Goldman, and contributed to ergodic and counting results that resonate with theorems by Gregory Margulis and Maryam Mirzakhani.

Labourie also developed techniques in geometric analysis for studying pseudo-holomorphic curves and variational problems influenced by methods from Mikhael Gromov's symplectic topology, and intersected with areas advanced by Richard Hamilton and Grigori Perelman in geometric flows. His framework influenced ongoing research in higher Teichmüller theory carried forward by researchers like Anna Wienhard, Oscar Garcia-Prada, Wolfgang Goldman, and François Guéritaud.

Awards and honors

Labourie received recognition including the Sophie Germain Prize and the Élie Cartan Prize from mathematical societies connected to the Institut Henri Poincaré and the Académie des Sciences. He was an invited speaker at the International Congress of Mathematicians and held memberships or visiting fellowships at the Institute for Advanced Study, the Institut des Hautes Études Scientifiques, and national academies linked to the Académie des Sciences (France). His work earned citations in award committees alongside laureates of the Fields Medal, the Wolf Prize, and the Abel Prize.

Selected publications

- Labourie, F., title treating Anosov flows and geometric structures, publication in journals like Inventiones Mathematicae and Journal of Differential Geometry; collaborations with authors connected to Maryam Mirzakhani, William Goldman, Anna Wienhard. - Labourie, F., papers on Hitchin representations and positivity in higher Teichmüller theory, appearing in proceedings of the American Mathematical Society and collections from Institute for Advanced Study programs. - Labourie, F., work on convex projective structures and dynamics, published in venues associated with the Clay Mathematics Institute and cited alongside research by Benoist and Guichard.

Category:French mathematicians Category:Differential geometers Category:Living people