November 14, 1919 - July 10, 2007

Paulette Libermann was born in Paris, France. At the age of 19 she entered l'École de Sèvres (also referred to as "École Normale Supérieure de Jeunes Filles"), a school for women to prepare them to become teachers in a secondary school for girls (at this time in France only women could teach to girls). By the time she completed her studies two years later, however, new anti-Semitic legislation prevented her from taking the *agrégation* in mathematical sciences (a competitive examination for positions in the public education system). Élie Cartan, one of the leading French mathematicians and a Professor of Higher Geometry at École Normale Supérieure, suggested that Libermann begin doing mathematical research under his direction.

In June 1942 Libermann was forced to move with her parents and two sisters to Lyon, where she gave private lessons. After the liberation of Lyon in 1944, she returned to the l'École de Sèvres and finally completed her agrégation in mathématiques (juenes filles). From 1945 to 1947 she studied at Oxford. In 1947 she began teaching at Lycée de Jeunes Filles, a school for girls in Strasbourg. At the same time, again with the encouragement of Élie Cartan, she began working under the direction of Charles Ehresmann at the Université Louis Pasteur-Strasbourg. Her first joint paper with Ehresmann appeared in 1949. Twelve more publications followed, culminating in her thesis, "Sur le problème d'équivalence de certaines structures infinitésimales," in 1953. Michèle Audin writes:

"In her thesis...can be found a number of things which lie now at the bases of symplectic geometry—which was not as fashionable then as it is today. For instance, she investigated foliations of symplectic manifolds and the local structure of the manifold together with certain foliations (a generalization of Darboux's theorem); she defined what Alan Weinstein would twenty years later call the affine structure of a Lagrangian foliation (this is at the basis of the theory of integrable systems); she investigated the almost-complex structures on a symplectic manifold that would turn out to be very useful, thirty years later, when Mikhael Gromov introduced and made such beautiful use of his pseudo-holomorphic curves, creating symplectic topology."

The thesis was published in Annali di Matematica Pura ed Applicata in 1954. The first part is an exposition of Cartan's theory of equivalence and the second part contains a detailed study of a number of special cases.

Upon receiving her Ph.D., Libermann joined the faculty at the University of Rennes where she continued her work in differential geometry. In 1966 she was appointed a professor at the University of Paris, becoming one of the few female professors of mathematics in a French university. She continued to be an influential and productive researcher, continuing the work of Cartan and Ehresmann and publishing over 70 papers, the last appearing shortly before her death in 2007. In 1987 Libermann and Charles-Michel Marle wrote *Symplectic Geometry and Analytical Mechanics*, one of the first textbooks on symplectic geometry and its application to Hamiltonian mechanics. An energetic traveler, Libermann spoke at numerous conferences around the world. She was also a visitor at many universities and research centers, including Oxford University, the University of California at Berkeley, the Mathematical Sciences Research Institute, and the National Institute of Pure and Applied Mathematics in Rio de Janeiro, Brazil.

- Audin, Michele. "Differential Geometry, Strasbourg, 1953", Notices of the AMS, vol. 55, no. 3 (March 2008), 366-370.
- Ehresmann, Andree C. "Sur Paulette Libermann (1919-2007)," Cah. Topol. Geom. Differ. Categ., vol. 48, no. 4 (2007), 270-274.
- Marle, Charles-Michel. "Hommage á Paulette Libermann," Gazette des Mathématiciens, no. 114 (October 2007).
- Kosmann-Schwarzbach, Y. "Paulette Libermann," Gazette des Mathématiciens, no. 114 (October 2007).
- Chaperon, Marc. "Souvenirs de Paulette Libermann," Images des MathÃ©matiques, CNRS, 2009. http://images.math.cnrs.fr/Souvenirs-de-Paulette-Libermann.html [ An English translation appeared in Eur. Math. Soc. Newsl. No. 77 (2010), 31-32]
- Chaperon, Marc. "En souvenir de Paulette Libermann" (In memory of Paulette Libermann), Gazette des Mathématiciens, No. 122 (2009), 63-90
- Chaperon, Marc. "En souvenir de Paulette Libermann, II" (In memory of Paulette Libermann, II), Gazette des Mathématiciens, No. 123 (2010), 49-66
- Kramer, Edna.
*The Nature and Growth of Modern Mathematics*, Hawthorn Books, Inc., New York, 1970, 711-712. - Paulette Libermann: Heritage et descendance website (in French)
- MathSciNet [subscription required]
- Author Profile at zbMath
- Mathematics Genealogy Project

Photo Credit: Photograph is used with permission of Paulette Libermann's niece, Corinne Mounier-Veil. It was taken by Libermann's great-niece, Clémentine Mounier.