Jean-Marie Souriau (3 June 1922,

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

– 15 March 2012,

Aix-en-Provence Aix-en-Provence (, , ; oc, label= Provençal, Ais de Provença in classical norm, or in Mistralian norm, ; la, Aquae Sextiae), or simply Aix ( medieval Occitan: ''Aics''), is a city and commune in southern France, about north of Marseille. ...

) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He was one of the pioneers of modern

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 differential form, closed, nondegenerate form, nondegenerate different ...

Education and career

Souriau started studying mathematics in 1942 at

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

in Paris. In 1946 he was a research fellow of

CNRS The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 ...

and an engineer at

ONERA The Office National d'Etudes et de Recherches Aérospatiales (ONERA) is the French national aerospace research centre. It is a public establishment with industrial and commercial operations, and carries out application-oriented research to supp ...

. His PhD thesis, defended in 1952 under the supervision of Joseph Pérès and

André Lichnerowicz André Lichnerowicz (January 21, 1915, Bourbon-l'Archambault – December 11, 1998, Paris) was a noted France, French Differential geometry and topology, differential geometer and Mathematical physics, mathematical physicist of Poland, Polish desc ...

, was entitled "''Sur la stabilité des avions''" (On the stability of planes). Between 1952 and 1958 he worked at Institut des Hautes Études in

Tunis ''Tounsi'' french: Tunisois , population_note = , population_urban = , population_metro = 2658816 , population_density_km2 = , timezone1 = CET , utc_offset1 ...

, and since 1958 he was Professor of Mathematics at the

University of Provence The University of Provence Aix-Marseille I (french: Université de Provence) was a public research university mostly located in Aix-en-Provence and Marseille. It was one of the three Universities of Aix-Marseille and was part of the Academy of ...

Marseille Marseille ( , , ; also spelled in English as Marseilles; oc, Marselha ) is the prefecture of the French department of Bouches-du-Rhône and capital of the Provence-Alpes-Côte d'Azur region. Situated in the camargue region of southern Franc ...

. In 1981 he was awarded the Prix Jaffé of the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

Research

Souriau contributed to the introduction and the development of many important concepts in

, arising from classical and

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

. In particular, he introduced the notion of

moment map In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the ac ...

, gave a classification of the

homogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...

symplectic manifold In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M , equipped with a closed nondegenerate differential 2-form \omega , called the symplectic form. The study of symplectic manifolds is called sympl ...

s (now known as the Kirillov- Kostant-Souriau theorem), and investigated the

coadjoint action In mathematics, the coadjoint representation K of a Lie group G is the dual of the adjoint representation. If \mathfrak denotes the Lie algebra of G, the corresponding action of G on \mathfrak^*, the dual space to \mathfrak, is called the coadj ...

of a

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

, which led to the first geometric interpretation of

spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...

at a classical level. He also suggested a program of

geometric quantization In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a wa ...

and developed a more general approach to

differentiable manifold In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One ma ...

s by means of diffeologies. Souriau published more than 50 papers in peer-review scientific journals, as well as three monographs, on

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrices. ...

, on relativity and on

geometric mechanics Geometric mechanics is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid bodies to fluid mechanics to control theory. Geometric mechanics applies principally to systems f ...

. He supervised 9 PhD students.

References

External links

Jean-Marie Souriau official website
(the website hosts copies of many of Souriau's works) * Ray F. Streater
Souriau
* Patrick Iglesias-Zemmour

(in French) * In Memoriam Conference 2012
Web site
* "Structure des Systèmes Dynamiques
Anniversary Conference 2019

Interview of Jean-Marie Souriau by Laurence Honnorat
on

YouTube YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by ...

(in French) {{DEFAULTSORT:Souriau, Jean-Marie 1922 births 2012 deaths French mathematicians École Normale Supérieure alumni University of Provence faculty