Michèle Vergne (born August 29, 1943, in L’Isle-Adam, Val d´Oise) is a French mathematician, specializing in analysis and representation theory.

Life and work

Michèle Vergne studied from 1962 to 1966 at the École Normal Supérieure de jeunes filles, which today is part of the ENS. She wrote her diploma thesis in 1966 with

Claude Chevalley Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a foundin ...

, entitled "Variété des algèbres de Lie nilpotentes" and her doctoral thesis in 1971 under the supervision of

Jacques Dixmier Jacques Dixmier (born 24 May 1924) is a French mathematician. He worked on operator algebras, especially C*-algebras, and wrote several of the standard reference books on them, and introduced the Dixmier trace and the Dixmier mapping. Biograph ...

("Recherches sur les groupes et les algèbres de Lie") at the University of Paris. She is currently Directeur de Recherche at CNRS. Vergne worked in the construction of unitary representations of

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 additio ...

s using

coadjoint orbit In mathematics, the coadjoint representation K of a Lie group G is the dual of the adjoint representation. If \mathfrak denotes the Lie algebra of G, the corresponding action of G on \mathfrak^*, the dual space to \mathfrak, is called the coadjoint ...

s of the Lie algebras. She proved a generalized Poisson summation formula (called the Poisson-Plancherel formula), which is the integral of a function on adjoint orbits with their Fourier transformation integrals on coadjoint "quantized" orbits. Further, she studied the index theory of elliptic differential operators and generalizations of this to equivariant cohomology. With Nicole Berline, it became a link between Atiyah-Bott fixed-point formulas and Kirillov character formula in 1985.American Journal Mathematics, Bd. 107, S. 1159 The theory has applications to physics (e.g., some works of Edward Witten). In addition she also worked in the

geometry of numbers Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in \mathbb R^n, and the study of these lattices provides fundamental information ...

; more specifically, the number of integer points in convex polyhedra. With

Masaki Kashiwara is a Japanese mathematician. He was a student of Mikio Sato at the University of Tokyo. Kashiwara made leading contributions towards algebraic analysis, microlocal analysis, D-module, ''D''-module theory, Hodge theory, sheaf theory and represent ...

, she formulated a conjecture about the combinatorial structure of the enveloping algebras of

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

s. Since 1997, she is a member of the Académie des sciences. She received the Prix Ampère in 1997. She is a member of The American Academy of Arts and Sciences. In 1992, she gave a plenary lecture at the first

European Congress of Mathematics The European Congress of Mathematics (ECM) is the second largest international conference of the mathematics community, after the International Congresses of Mathematicians (ICM). The ECM are held every four years and are timed precisely betwee ...

in Paris (Cohomologie equivariante et formules de carácteres). In 2006 she gave a plenary lecture at the International Congress of mathematics in Madrid (Applications of Equivariant Cohomology) and in 1983 she was an invited speaker at the ICM in Warsaw (Formule de Kirilov et indice de l'opérateur de Dirac). In 2008 she was Emmy-Noether - visiting professor at the University of Göttingen. She is a fellow of the American Mathematical Society. Michèle Vergne was married to

Victor Kac Victor Gershevich (Grigorievich) Kac (russian: link=no, Виктор Гершевич (Григорьевич) Кац; born 19 December 1943) is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-disco ...

. They have a daughter, Marianne Kac-Vergne, professor of American civilization at the university of Picardie.

Selected publications

* with G. Lion: ''The Weil representation, Maslov Index and Theta Series'', Birkhäuser 1980 * with Nicole Berline, Ezra Getzler: ''Heat kernels and Dirac operators'', Springer, Grundlehren der mathematischen Wissenschaften, 1992, 2004
''Quantification geometrique et reduction symplectique''
Seminar Bourbaki 2000/1
''Représentations unitaires des groupes de Lie résolubles.''
Seminar Bourbaki, 1973/4 * with

Michel Duflo Michel Duflo (born 15 August 1943) is a French mathematician who works in the representation theory of Lie groups. Life From 1962, Duflo studied at the École normale supérieure and received a doctorate under the supervision of Jacques Dixm ...

''Sur la représentation coadjointe d'une algèbre de Lie ''
Compositio Mathematica 1974
''Applications of Equivariant Cohomology''
ICM 2006

References

*The original article was a (machine) translation of the corresponding German article.

External links

Interview with Vergne
in the ''Gazette des Mathématiciens'' (p. 46)

Personal site
{{DEFAULTSORT:Vergne, Michele 1943 births Living people People from L'Isle-Adam, Val-d'Oise 20th-century French mathematicians 21st-century French mathematicians Fellows of the American Mathematical Society French women mathematicians 20th-century women mathematicians 21st-century women mathematicians 20th-century French women 21st-century French women