Jean Leray
Encyclopedia
Jean Leray was a French
mathematician
, who worked on both partial differential equation
s and algebraic topology
.
He was born in Chantenay-sur-Loire (today part of Nantes
). He studied at École Normale Supérieure
from 1926 to 1929. He received his Ph.D. in 1933. Leray wrote an important paper that founded the study of weak solutions of the Navier–Stokes equations. Together with Juliusz Schauder
, he discovered a topological invariant, now called the Leray–Schauder degree, which they applied to prove the existence of solutions for partial differential equations lacking uniqueness.
From 1938 to 1939 he was professor at the University of Nancy. He did not join the Bourbaki group, although he was close with its founders.
His main work in topology
was carried out while he was in a prisoner of war
camp in Edelbach, Austria
from 1940 to 1945. He concealed his expertise on differential equations, fearing that its connections with applied mathematics
could lead him to be asked to do war work.
Leray's work of this period proved seminal to the development of spectral sequence
s and sheaves
. These were subsequently developed by many others, each separately becoming an important tool in homological algebra
.
He returned to work on partial differential equations from about 1950.
He was professor at the University of Paris
from 1945 to 1947, and then at the Collège de France
until 1978.
He was awarded the Malaxa Prize (Romania
, 1938), the Grand Prix in mathematical sciences (French Academy of Sciences
, 1940), the Feltrinelli Prize
(Accademia dei Lincei
, 1971), the Wolf Prize in Mathematics
(Israel
, 1979), and the Lomonosov Gold Medal
(Moscow
, 1988).
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, who worked on both partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s and algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
.
He was born in Chantenay-sur-Loire (today part of Nantes
Nantes
Nantes is a city in western France, located on the Loire River, from the Atlantic coast. The city is the 6th largest in France, while its metropolitan area ranks 8th with over 800,000 inhabitants....
). He studied at École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
from 1926 to 1929. He received his Ph.D. in 1933. Leray wrote an important paper that founded the study of weak solutions of the Navier–Stokes equations. Together with Juliusz Schauder
Juliusz Schauder
Juliusz Paweł Schauder was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equation and mathematical physics.Born on September 21, 1899 in Lemberg, he had to fight in World War I right after his graduation from school...
, he discovered a topological invariant, now called the Leray–Schauder degree, which they applied to prove the existence of solutions for partial differential equations lacking uniqueness.
From 1938 to 1939 he was professor at the University of Nancy. He did not join the Bourbaki group, although he was close with its founders.
His main work in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
was carried out while he was in a prisoner of war
Prisoner of war
A prisoner of war or enemy prisoner of war is a person, whether civilian or combatant, who is held in custody by an enemy power during or immediately after an armed conflict...
camp in Edelbach, Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
from 1940 to 1945. He concealed his expertise on differential equations, fearing that its connections with applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
could lead him to be asked to do war work.
Leray's work of this period proved seminal to the development of spectral sequence
Spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations...
s and sheaves
Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be restricted to smaller open sets, and the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of...
. These were subsequently developed by many others, each separately becoming an important tool in homological algebra
Homological algebra
Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and...
.
He returned to work on partial differential equations from about 1950.
He was professor at the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
from 1945 to 1947, and then at the Collège de France
Collège de France
The Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles...
until 1978.
He was awarded the Malaxa Prize (Romania
Romania
Romania is a country located at the crossroads of Central and Southeastern Europe, on the Lower Danube, within and outside the Carpathian arch, bordering on the Black Sea...
, 1938), the Grand Prix in mathematical sciences (French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
, 1940), the Feltrinelli Prize
Feltrinelli Prize
The Feltrinelli Prize is a prestigious award for achievement in the arts, music, literature, history, philosophy, medicine, and physical and mathematical sciences...
(Accademia dei Lincei
Accademia dei Lincei
The Accademia dei Lincei, , is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy....
, 1971), the Wolf Prize in Mathematics
Wolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
(Israel
Israel
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...
, 1979), and the Lomonosov Gold Medal
Lomonosov Gold Medal
The Lomonosov Gold Medal, named after Russian scientist and polymath Mikhail Lomonosov, is awarded each year since 1959 for outstanding achievements in the natural sciences and the humanities by the USSR Academy of Sciences and later the Russian Academy of Sciences . Two medals are awarded...
(Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
, 1988).
See also
- Leray spectral sequenceLeray spectral sequenceIn mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. The formulation was of a spectral sequence, expressing the relationship holding in sheaf cohomology between two topological spaces X and Y, and set up by a continuous...
- Leray coverLeray coverIn mathematics, a Leray cover is a cover which allows for easy calculation of cohomology.Sheaf cohomology measures the extent to which a locally exact sequence on a fixed topological space, for instance the deRham sequence, fails to be globally exact. Its definition, using derived functors, is...
- Leray's theoremLeray's theoremIn algebraic geometry, Leray's theorem relates abstract sheaf cohomology with Čech cohomology.Let \mathcal F be a sheaf on a topological space X and \mathcal U an open cover of X...
- Leray–Hirsch theorem
External links
- "Jean Leray (1906–1998)", by Armand BorelArmand BorelArmand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993...
, Gennadi M. Henkin, and Peter D. Lax, Notices of the American Mathematical Society, vol. 47, no. 3, March 2000. - Jean Leray Short biography