Roger Godement
Encyclopedia
Roger Godement is a French
mathematician
, known for his work in functional analysis
, and also his expository books.
He started as a student at the École normale supérieure
in 1940, where he became a student of Henri Cartan
. He started research into harmonic analysis
on locally compact abelian groups, 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
s published in 1952 proved very influential in subsequent work, particularly that of Harish Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic group
s was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra.
He was an active member of the Bourbaki group 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); as a non-specialist, he managed to write an enduring classic. It introduced the technical method of flasque resolutions. It has also been credited as the place in which a comonad can first be discerned.
He also wrote texts on Lie group
s, abstract algebra
and mathematical analysis
.
French people
The French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...
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....
, known for his work in functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, and also his expository books.
He started as a student at the École normale supérieure
École normale supérieure
An école normale supérieure or ENS is a type of publicly funded higher education in France. A portion of the student body who are French civil servants are called Normaliens....
in 1940, where he became a student of Henri Cartan
Henri Cartan
Henri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan.-Life:...
. He started research into harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
on locally compact abelian groups, 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
Spherical function
Spherical function can refer to* Spherical harmonics*Zonal spherical function...
s published in 1952 proved very influential in subsequent work, particularly that of Harish Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic group
Arithmetic group
In mathematics, an arithmetic group in a linear algebraic group G defined over a number field K is a subgroup Γ of G that is commensurable with G, where O is the ring of integers of K. Here two subgroups A and B of a group are commensurable when their intersection has finite index in each of them...
s was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra.
He was an active member of the Bourbaki group 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); as a non-specialist, he managed to write an enduring classic. It introduced the technical method of flasque resolutions. It has also been credited as the place in which a comonad can first be discerned.
He also wrote texts on Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s, abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
and mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
.