Michel Paul Lazard (5 December 1924 – 15 September 1987) was a French mathematician who worked on the theory of

Lie groups 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 ...

in the context of

p-adic analysis In mathematics, ''p''-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of ''p''-adic numbers. The theory of complex-valued numerical functions on the ''p''-adic numbers is part of the theory of lo ...

Career and research

Born in

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 ...

, Lazard studied at the

University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

–

Sorbonne Sorbonne may refer to: * Sorbonne (building), historic building in Paris, which housed the University of Paris and is now shared among multiple universities. *the University of Paris (c. 1150 – 1970) *one of its components or linked institution, ...

, where he obtained his Ph.D. in 1954 under the direction of

Albert Châtelet Albert Châtelet (24 October 1883 – 30 June 1960) was a French politician and mathematician. Biography Châtelet was a student at the École normale supérieure (Paris) from 1905 to 1908, succeeding to the Agrégation (a highly selective compe ...

, with thesis titled "Sur les groupes nilpotents et les anneaux de Lie". Subsequently he was a professor at the

University of Poitiers The University of Poitiers (UP; french: Université de Poitiers) is a public university located in Poitiers, France. It is a member of the Coimbra Group. It is multidisciplinary and contributes to making Poitiers the city with the highest studen ...

and the

University of Paris 7 Paris Diderot University, also known as Paris 7 (french: Université Paris Diderot), 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 197 ...

. He died of suicide at the age of 63. His work took on a life of its own in the hands of

Daniel Quillen Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic ''K''-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 197 ...

in the late 20th century. Quillen's discovery, that a ring Lazard used to classify formal group laws was isomorphic to an important ring in topology, led to the subject of

chromatic homotopy theory In mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic" point of view, which is based on Quillen's work relating cohomology theories to formal groups ...

. Lazard's self-contained treatise on one-dimensional formal groups also gave rise to the field of p-divisible groups. His major contributions were: * The classification of

p-adic 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 add ...

s: every p-adic Lie group is a closed subgroup of

_n(\mathbb_p)

. * The classification of (1-dimensional commutative)

formal group In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one o ...

s. * The universal formal group law coefficient ring (

Lazard's universal ring In mathematics, Lazard's universal ring is a ring introduced by Michel Lazard in over which the universal commutative one-dimensional formal group law is defined. There is a universal commutative one-dimensional formal group law over a universal ...

) is a

polynomial ring In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) ...

. * The concept of "analyseurs", reinvented by

J. Peter May Jon Peter May (born September 16, 1939 in New York) is an American mathematician working in the fields of algebraic topology, category theory, homotopy theory, and the foundational aspects of spectra. He is known, in particular, for the May ...

under the name

operad In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given an operad O, one define ...

Awards and honours

In 1958 Lazard was the first recipient of the ''Prix Audin'', named after the young French mathematician

Maurice Audin Maurice Audin (14 February 1932 – c. 21 June 1957) was a renowned French mathematics assistant at the University of Algiers, a member of the Algerian Communist Party and an activist in the anticolonialist cause, who died under torture by the Fr ...

, who had been assassinated in Algeria. In 1972, he was awarded the

Prix Poncelet The Poncelet Prize (french: Prix Poncelet) is awarded by the French Academy of Sciences. The prize was established in 1868 by the widow of General Jean-Victor Poncelet for the advancement of the sciences. It was in the amount of 2,000 francs (as o ...

by the

Académie des Sciences The French Academy of Sciences (French: ''Académie des 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. It was at the ...

for his work on algebra.

Notes

References

* * New edition of ''Séminaire C. Chevalley'', 1956–1958: Classification des groupes de Lie algébriques, Secrétariat Math., 11 rue Pierre Curie, Paris, 1958. * * * * * {{DEFAULTSORT:Lazard, Michel 1924 births 1985 deaths 20th-century French mathematicians Group theorists Scientists from Paris University of Paris alumni Academic staff of the University of Poitiers Academic staff of the University of Paris