Paulette Libermann (14 November 1919 – 10 July 2007) was a French mathematician, specializing in

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

Early life and education

Libermann was one of three sisters born to a family of Russian-Ukrainian

Yiddish Yiddish, historically Judeo-German, is a West Germanic language historically spoken by Ashkenazi Jews. It originated in 9th-century Central Europe, and provided the nascent Ashkenazi community with a vernacular based on High German fused with ...

-speaking Jewish immigrants to Paris. After attending the

Lycée Lamartine The Lycée Lamartine is a French institute of secondary education in the 9th arrondissement of Paris. It combines a ''collège'', a ''lycée'', and a ''Classe préparatoire aux grandes écoles'' (prep school for the ''Grandes écoles''). The sch ...

, she began her university studies in 1938 at the

École normale supérieure de jeunes filles The ''École normale supérieure de jeunes filles'' (also, ''École normale supérieure de Sèvres'') was a French institute of higher education, in Sèvres, now a commune in the suburbs of Paris. The school educated girls only, especially as te ...

, a college in

Sèvres Sèvres (, ) is a French Communes of France, commune in the southwestern suburbs of Paris. It is located from the Kilometre zero, centre of Paris, in the Hauts-de-Seine department of the Île-de-France region. The commune, which had a populatio ...

for training women to become school teachers. Due to the reforms of the new director

Eugénie Cotton Eugénie Cotton (13 October 1881 – 16 June 1967) was a French scientist, socialist, women's rights advocate and was active in the resistance. She was awarded the Stalin Peace Prize in 1951, Knight of the Legion of Honor, and the Gold medal fro ...

, who wanted her school to be at the same level of

École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...

, Libermann was taught by leading mathematicians including

Élie Cartan Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He ...

Jacqueline Ferrand Jacqueline Lelong-Ferrand (17 February 1918, Alès, France – 26 April 2014, Sceaux, France) was a French mathematician who worked on conformal representation theory, potential theory, and Riemannian manifolds. She taught at universities in ...

and

André Lichnerowicz André Lichnerowicz (; January 21, 1915, Bourbon-l'Archambault – December 11, 1998, Paris) was a French differential geometer and mathematical physicist. He is considered the founder of modern Poisson geometry. Biography His grandfather Jan f ...

.. Two years later, upon completion of her studies, she was prevented from taking the

agrégation In France, the () is the most competitive and prestigious examination for civil service in the French public education A state school, public school, or government school is a primary school, primary or secondary school that educates all stu ...

and becoming a teacher because of the anti-Jewish laws instituted by the

German occupation German-occupied Europe, or Nazi-occupied Europe, refers to the sovereign countries of Europe which were wholly or partly militarily occupied and civil-occupied, including puppet states, by the (armed forces) and the government of Nazi Germany at ...

. However, thanks to a scholarship provided by Cotton, she began doing research under Cartan's supervision. In 1942, she and her family escaped Paris for

Lyon Lyon (Franco-Provençal: ''Liyon'') is a city in France. It is located at the confluence of the rivers Rhône and Saône, to the northwest of the French Alps, southeast of Paris, north of Marseille, southwest of Geneva, Switzerland, north ...

, where they hid from the persecutions by

Klaus Barbie Nikolaus Barbie (25 October 1913 – 25 September 1991) was a German officer of the ''Schutzstaffel'' and ''Sicherheitsdienst'' who worked in Vichy France during World War II. He became known as the "Butcher of Lyon" for having personally tortu ...

for two years. After the

liberation of Paris The liberation of Paris () was a battle that took place during World War II from 19 August 1944 until the German garrison surrendered the French capital on 25 August 1944. Paris had been occupied by Nazi Germany since the signing of the Armisti ...

in 1944, she returned to Sèvres and completed her studies, obtaining the agrégation.

Career

Libermann taught briefly in a school at

Douai Douai ( , , ; ; ; formerly spelled Douay or Doway in English) is a city in the Nord (French department), Nord département in northern France. It is a Subprefectures in France, sub-prefecture of the department. Located on the river Scarpe (rive ...

, and then got a scholarship to study at

Oxford University The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...

between 1945 and 1947, where she obtained a bachelor's degree under the supervision of

J. H. C. Whitehead John Henry Constantine Whitehead FRS (11 November 1904 – 8 May 1960), known as "Henry", was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai (then known as Madras), in India, and died in Princet ...

. From 1947 to 1951 she hold a teaching position at a school for girls in

Strasbourg Strasbourg ( , ; ; ) is the Prefectures in France, prefecture and largest city of the Grand Est Regions of France, region of Geography of France, eastern France, in the historic region of Alsace. It is the prefecture of the Bas-Rhin Departmen ...

. However, at the encouragement of Élie Cartan, during this period she also continued her research at

Université Louis Pasteur Louis Pasteur University (, ULP), also known as Strasbourg I, was a large university in Strasbourg, Alsace, France. As of 15 January 2007, there were 18,847 students enrolled at the university, including around 3,000 foreign students. Researc ...

. In 1951 she left teaching for a research position at the

Centre national de la recherche scientifique The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

, and in 1953 she completed her doctoral thesis, entitled ''Sur le problème d’équivalence de certaines structures infinitésimales''

n the equivalence problem of certain infinitesimal structures N, or n, is the fourteenth letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages, and others worldwide. Its name in English is ''en'' (pronounced ), plural ''ens''. History ...

under the supervision of

Charles Ehresmann Charles Ehresmann (19 April 1905 – 22 September 1979) was a German-born French mathematician who worked in differential topology and category theory. He was an early member of the Bourbaki group, and is known for his work on the differentia ...

. After her PhD, Libermann was appointed assistant professor at the

University of Rennes The University of Rennes (French: ''Université de Rennes'') is a public university, public research university located in Rennes, Upper Brittany, France. Originally founded in 1460, the university was split into two universities in 1970: Univers ...

in 1954 and full professor at the same university in 1958. In 1966 she moved to the

University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...

, and when the university split in 1968, she joined

Paris Diderot University Paris Diderot University, also known as Paris 7 (), was a French university located in Paris, France. It was one of the inheritors of the historic University of Paris, which was split into 13 universities in 1970. Paris Diderot merged with Pari ...

, from which she retired in 1986.

Research

Libermann's research involved many different aspects of

and

global analysis In mathematics, global analysis, also called analysis on manifolds, is the study of the global and topological properties of differential equations on manifolds and vector bundles. Global analysis uses techniques in infinite-dimensional manifold ...

... In particular, she worked on G-structures and

Cartan's equivalence method In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if ''M'' and ''N'' are two Riemannian manifolds with metrics ' ...

Lie groupoids A lie is an assertion that is believed to be false, typically used with the purpose of deceiving or misleading someone. The practice of communicating lies is called lying. A person who communicates a lie may be termed a liar. Lies can be int ...

and Lie pseudogroups, higher-order

connections Connections may refer to: * Connection (disambiguation), plural form Television * '' Connections: An Investigation into Organized Crime in Canada'', a documentary television series * ''Connections'' (British TV series), a 1978 documentary tele ...

, and

contact geometry In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently, such a distribution ...

. In 1987 she wrote together with Charles-Michel Marle one of the first textbooks on

symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the ...

and

analytical mechanics In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related formulations of classical mechanics. Analytical mechanics uses '' scalar'' properties of motion representing the sy ...

Selected publications

References

{{DEFAULTSORT:Libermann, Paulette 1919 births 2007 deaths 20th-century French Jews French mathematicians French women mathematicians Differential geometers 20th-century French women scientists