Michèle Vergne

Michèle Vergne ( born August 29, 1943 in L' Isle- Adam, Val d' Oise ) is a French mathematician who deals with analysis and representation theory.

Life and work

Michèle Vergne studied from 1962 to 1966 at the École normale supérieure de jeunes filles, which is part of the ENS today. Her thesis she wrote in 1966 with Claude Chevalley, it was entitled " vaudeville of algebres de Lie nilpotent " and her PhD in 1971 with Jacques Dixmier ( " Recherches sur les groupes et les algebres de Lie" ) at the University of Paris. From 1967 she was Attaché de Recherches at the CNRS. 1971/2 she was a lecturer at the University of California, Berkeley. From 1972, she was Chargé de Recherches at the CNRS, Maitre de Recherches in 1976 of the CNRS and from 1981 Directeur de Recherche. 1975/6 and 1977 to 1979 she was a visiting professor at the Massachusetts Institute of Technology (MIT ) in 1979 and Associate Professor from 1981 to 1986 professor at MIT. She is currently Directeur de Recherche at the CNRS.

Vergne focused on the construction of unitary representations of Lie groups using koadjungierter orbits of the Lie algebra. She proved a generalized Poisson sum formula (of their Poisson - Plancherel formula called ), the integrals of a function on the adjoint orbit with integrals of its Fourier transform on koadjungierten " quantized " orbits in relationship sets.

Next she worked on the index theory of elliptic differential operators and generalizations of this and with Equivarianter cohomology, in the cohomological aspects of a Lie group acting on a manifold, be related to the cohomology of the manifold in relationship. With Nicole Berline they presented in 1985 a combination of Atiyah - Bott fixed point formula with the character formula for the Lie group of Kirillov ago. The theory also has applications in physics (e.g., Edward Witten).

In addition, they also dealt with the geometry of numbers, issue was the number of integer points in convex polyhedra.

With Masaki Kashiwara they formulated a conjecture about the combinatorial structure of the envelope algebras of Lie algebras.

Since 1997 she is a member of the Académie des sciences, the Prix Bordin it in 1980 and the Prix Ampere she received in 1997. She is a member of the American Academy of Arts and Sciences. In 1992 he gave a plenary lecture at the first European Congress of Mathematicians in Paris ( equivariant cohomology et formules de caracteres ). In 2006 she gave a plenary lecture at the International Congress of Mathematicians in Madrid ( Applications of Equivariant Cohomology ) and in 1983 she was 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.

Writings

• With G. Lion: The Weil representation, Maslov index and Theta Series, Birkhauser 1980
• With Nicole Berline, Ezra Getzler: Heat kernels and Dirac operators, Springer, basic teachings of the mathematical sciences, 1992, 2004
• Quantification geometrique et reduction symplectique, Seminar Bourbaki 2000/1
• Représentations unit aires of the groupes de Lie résolubles. , Seminar Bourbaki, 1973/4
• With Michel Duflo, Jacques Dixmier: Sur la représentation coadjointe d'une algèbre de Lie, Compositio Mathematica 1974
• Applications of Equivariant Cohomology, ICM 2006