Michèle Vergne

Michèle Vergne is a French mathematician, born on 29 August 1943 in L'Isle-Adam, who works in analysis and representation theory. She studied at the École Normale Supérieure de jeunes filles from 1962 to 1966, wrote her diploma thesis in 1966 with Claude Chevalley on varieties of nilpotent Lie algebras, and completed her doctoral thesis in 1971 under Jacques Dixmier at the University of Paris. Her work builds unitary representations of Lie groups from coadjoint orbits of their Lie algebras, and includes a generalised Poisson summation formula called the Poisson-Plancherel formula. She also studied the index theory of elliptic differential operators and its extension to equivariant cohomology; with Nicole Berline in 1985 this linked the Atiyah-Bott fixed-point formulas to the Kirillov character formula. In the geometry of numbers she counted integer points in convex polyhedra, and with Masaki Kashiwara she formulated a conjecture on the combinatorial structure of enveloping algebras of Lie algebras. She is a Directeur de Recherche at CNRS, has belonged to the Académie des sciences since 1997, and received the Prix Ampère in 1997.