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, mathematical structure, structure, space, Mathematica ...
, 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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...
as well as his expository books.
Biography
Godement started as a student at the
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 ...
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 investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...
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 function
A sphere (from Greek , ) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ''center'' o ...
s published in 1952 proved very influential in subsequent work, particularly that of
Harish-Chandra
Harish-Chandra (né Harishchandra) 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 ...
. 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 theor ...
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
* A ...
of a simple algebra.
He was an active member of the
Bourbaki group Bourbaki(s) may refer to :
Persons and science
* Charles-Denis Bourbaki (1816–1897), French general, son of Constantin Denis Bourbaki
* Colonel Constantin Denis Bourbaki (1787–1827), officer in the Greek War of Independence and serving in t ...
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 (: sheaves) 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 d ...
); 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 can first be discerned.
He also wrote texts on
Lie group
In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Eucli ...
s,
abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
and
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...
.
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
*
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
In mathematics, the term standard L-function refers to a particular type of automorphic L-function described by Robert P. Langlands.
Here, ''standard'' refers to the finite-dimensional representation r being the standard representation of the Langl ...
References
External links
*
*
{{DEFAULTSORT:Godement, Roger
1921 births
2016 deaths
French mathematicians
École Normale Supérieure alumni
Nicolas Bourbaki
Academic staff of Paris Diderot University
Scientists from Le Havre