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Roger Godement (; 1 October 1921 – 21 July 2016) 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 ...
, known for his work in
functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined ...
as well as his expository books.


Biography

Godement started as a student at the
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 1940, where he became a student of
Henri Cartan Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of c ...
. He started research into
harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an ex ...
on
locally compact abelian group In several mathematical areas, including harmonic analysis, topology, and number theory, locally compact abelian groups are abelian groups which have a particularly convenient topology on them. For example, the group of integers (equipped with the ...
s, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of
Harish-Chandra Harish-Chandra FRS (11 October 1923 – 16 October 1983) was an Indian American mathematician and physicist who did fundamental work in representation theory, especially harmonic analysis on semisimple Lie groups. Early life Harish-Chandra wa ...
. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of
arithmetic group In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example \mathrm_2(\Z). They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number the ...
s was a conjecture of his. He later worked with Jacquet on the
zeta function In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function : \zeta(s) = \sum_^\infty \frac 1 . Zeta functions include: * Airy zeta function, related to the zeros of the Airy function * ...
of a simple algebra. He was an active member of the
Bourbaki group Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure - PSL (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in ...
in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. His book ''Topologie Algébrique et Théorie des Faisceaux'' from 1958 was, as he said, a very unoriginal idea for the time (that is, to write an exposition of
sheaf theory In mathematics, a sheaf is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the data could ...
); as a non-specialist, he managed to write an enduring classic. It introduced the technical method of flasque resolutions, nowadays called Godement resolutions. It has also been credited as the place in which a
comonad In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is a monoid in the category of endofunctors. An endofunctor is a functor mapping a category to itself, and a monad is an ...
can first be discerned. He also wrote texts on
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,
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The te ...
and
mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied i ...
.


Selected publications

* *''Topologie algébrique et théorie des faisceaux.'' Hermann 1958, 1960. *''Cours d´algèbre.'' Hermann 1963, 1966. *''Algebra.'' Hermann 1968. * * *''Analyse mathématique.'' 4 vols., Springer-Verlag 1998–2001.


See also

*
Commutation theorem for traces In mathematics, a commutation theorem for traces explicitly identifies the commutant of a specific von Neumann algebra acting on a Hilbert space in the presence of a trace. The first such result was proved by Francis Joseph Murray and John von N ...
*
Plancherel theorem for spherical functions In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its final form to Harish-Chandra. It is a natural generalisation in non-commutative harmonic analysi ...
* Standard L-function


References


External links

* * {{DEFAULTSORT:Godement, Roger 1921 births 2016 deaths French mathematicians École Normale Supérieure alumni Nicolas Bourbaki Paris Diderot University faculty Scientists from Le Havre