Michèle Vergne

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Michèle Vergne is affiliated with the following schools: Paris Sciences et Lettres University, Massachusetts Institute of Technology

Michèle Vergne's AcademicInfluence.com Rankings

Michèle Vergne

Mathematics

#1261

World Rank

#2108

Historical Rank

Measure Theory

#2335

World Rank

#2793

Historical Rank

mathematics Degrees

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Mathematics

Why Is Michèle Vergne Influential?

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According to Wikipedia, Michèle Vergne 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, entitled "Variété des algèbres de Lie nilpotentes" and her doctoral thesis in 1971 under the supervision of Jacques Dixmier at the University of Paris. She is currently Directeur de Recherche at CNRS.

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Michèle Vergne's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Heat Kernels and Dirac Operators (1992) (2003)
On the Segal-Shale-Weil representations and harmonic polynomials (1978) (440)
The Weil representation, Maslov index, and theta series (1980) (385)
Analytic continuation of the holomorphic discrete series of a semi-simple Lie group (1976) (183)
Residue formulae, vector partition functions and lattice points in rational polytopes (1997) (162)
Lattice points in simple polytopes (1997) (126)
Arrangement of hyperplanes. I. Rational functions and Jeffrey-Kirwan residue (1999) (119)
Wave and Dirac operators, and representations of the conformal group (1977) (116)
An equivariant Riemann-Roch theorem for complete, simplicial toric varieties. (1997) (109)
Heat Kernels and Dirac Operators: Grundlehren 298 (1992) (107)
Restrictions and Expansions of Holomorphic Representations (1979) (105)
How to integrate a polynomial over a simplex (2008) (101)
Residue formulae for vector partitions and Euler-MacLaurin sums (2002) (101)
The Campbell-Hausdorff formula and invariant hyperfunctions (1978) (99)
Toric reduction and a conjecture of Batyrev and Materov (2003) (96)
Modular forms of weight 1/2 (1980) (92)
Representations of certain solvable Lie groups on Hilbert spaces of holomorphic functions and the ap (1973) (89)
Local Euler-Maclaurin formula for polytopes (2005) (81)
The Chern character of a transversally elliptic symbol and the equivariant index (1996) (67)
The Equivariant Index and Kirillov's Character Formula (1985) (66)
Kostant Partitions Functions and Flow Polytopes (2008) (62)
Counting Integer Flows in Networks (2003) (60)
The Orbit Method in Representation Theory (1990) (59)
Residues formulae for volumes and Ehrhart polynomials of convex polytopes. (2001) (58)
Applications of equivariant cohomology (2006) (52)
D-modules, Representation Theory, and Quantum Groups (1993) (52)
A computation of the equivariant index of the Dirac operator (1985) (50)
Volume Computation for Polytopes and Partition Functions for Classical Root Systems (2005) (48)
Index of transversally elliptic operators (2008) (47)
ON SOME EXPLICIT FORMULAS IN THE THEORY OF WEIL REPRESENTATION (2004) (43)
MULTIPLICITIES FORMULA FOR GEOMETRIC QUANTIZATION, PART II (1996) (41)
EQUIVARIANT INDEX FORMULAS FOR ORBIFOLDS (1996) (40)
Fourier Transforms of Orbits of the Coadjoint Representation (1983) (39)
Computation of the Highest Coefficients of Weighted Ehrhart Quasi-polynomials of Rational Polyhedra (2010) (38)
Geometric Quantization and Equivariant Cohomology (1994) (37)
Vector partition functions and index of transversally elliptic operators (2008) (36)
Non-Commutative Harmonic Analysis (1975) (36)
Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory (2010) (34)
Representations of Lie Groups and the Orbit Method (1983) (34)
A note on the Jeffrey-Kirwan-Witten localisation formula (1996) (34)
Functions on the shilov boundary of the generalized half plane (1979) (31)
Equivariant Dirac operators and differentiable geometric invariant theory (2014) (28)
Box splines and the equivariant index theorem (2010) (27)
Inequalities for Moment Cones of Finite-Dimensional Representations (2014) (26)
K-types and singular spectrum (1979) (25)
Witten Non Abelian Localization for Equivariant K-Theory, and the [𝑄,𝑅]=0 Theorem (2015) (24)
Convex polytopes and quantization of symplectic manifolds. (1996) (23)
On Rossmann's character formula for discrete series (1979) (22)
A proof of Bismut local index theorem for a family of Dirac operators (1987) (22)
Residue Formulae For Verlinde Sums, And For Number Of Integral Points In Convex Rational Polytopes (2003) (21)
The equivariant Chern character and index of G-invariant Operators (1992) (20)
Vector partition function and generalized Dahmen-Micchelli spaces (2008) (19)
Non Commutative Harmonic Analysis and Lie Groups (1981) (19)
Equivariant relative Thom forms and Chern characters (2007) (18)
A Poisson-Plancherel formula for semi-simple Lie groups (1982) (17)
Harmonically induced representations of solvable Lie groups (1985) (17)
The multiplicities of the equivariant index of twisted Dirac operators (2014) (17)
Paradan's wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator (2008) (16)
Vector partition functions and generalized dahmen and micchelli spaces (2010) (16)
The infinitesimal index (2010) (15)
ADMISSIBLE COADJOINT ORBITS FOR COMPACT LIE GROUPS (2015) (15)
Computation of dilated Kronecker coefficients (2016) (15)
Symmetry and causality properties of physical fields. (1978) (12)
Multiplicity of compact group representations and applications to Kronecker coefficients (2015) (12)
Hamiltonian manifolds and moment map (2011) (12)
Equivariant Chern characters with generalized coefficients (2008) (11)
ARRANGEMENT OF HYPERPLANES, II: THE SZENES FORMULA AND EISENSTEIN SERIES (2000) (11)
The Shale-Weil representation associated to a quadratic form (1980) (11)
Group representations on Hilbert spaces defined in terms of ∂b-cohomology on the Silov boundary of a Siegel domain (1976) (10)
Equivariant cohomology with generalized coefficients (2019) (10)
Infinitesimal index: cohomology computations (2010) (10)
The Horn inequalities from a geometric point of view (2016) (10)
The equivariant Todd genus of a complete toric variety, with Danilov condition (2006) (10)
Equivariant cohomology with generalized coefficients (2019) (10)
Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope (2007) (9)
Quantization of algebraic cones and Vogan’s conjecture (1998) (9)
On the localization theorem in equivariant cohomology (1997) (9)
Morris identities and the total residue for a system of type A r (2004) (9)
Kirillov's formula and Guillemin-Sternberg conjecture (2011) (8)
Mixed toric residues and tropical degenerations (2004) (8)
Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces (2013) (8)
The multiplier of θ (1980) (7)
Local asymptotic Euler-Maclaurin expansion for Riemann sums over a semi-rational polyhedron (2015) (7)
[$Q, R$] = 0 and Kostant partition functions (2010) (7)
Multiple Bernoulli series, an Euler-MacLaurin formula, and wall crossings (2010) (6)
Poisson summation formula and Box splines (2013) (6)
Coefficients of Sylvester's Denumerant (2013) (6)
INTERMEDIATE SUMS ON POLYHEDRA II: BIDEGREE AND POISSON FORMULA (2014) (6)
A homotopy for a complex of free Lie algebras (2011) (6)
QUILLEN'S RELATIVE CHERN CHARACTER IS MULTIPLICATIVE (2007) (5)
Horn inequalities and quivers (2018) (5)
The equivariant Riemann–Roch theorem and the graded Todd class (2016) (5)
Recurrence relations for Plancherel functions (1987) (4)
Asymptotic Expansion of the Heat Kernel (1992) (4)
Multiplicities of equivariant Spin$^c$ Dirac operators (2014) (4)
Horn conditions for Schubert positions of general quiver subrepresentations (2019) (3)
The universal covering group of SL(2,ℝ) (1980) (3)
Analytic continuation of a parametric polytope and wall-crossing (2011) (3)
Geometric Quantization in the Non-compact Setting (2011) (3)
Formal equivariant class, splines and multiplicities of the index of transversally elliptic operators (2012) (3)
Three Ehrhart quasi-polynomials (2014) (3)
Noncommutative Harmonic Analysis: In Honor Of Jacques Carmona (2012) (3)
The Index Bundle (1992) (3)
Horn conditions for quiver subrepresentations and the moment map (2019) (3)
Discrete series representations and K mulltiplicities for U(p,q): user's guide (2010) (2)
A remark on the convolution with the box spline (2011) (2)
Top Coefficients of the Denumerant (2013) (2)
Bouquets Revisited and Equivariant Elliptic Cohomology (2020) (2)
Asymptotic distributions associated to piecewise quasi-polynomials (2017) (2)
Some Comments on the Work of I. E. Segal on Group Representations (2002) (2)
Noncommutative Harmonic Analysis (2004) (2)
The Shimura correspondence (1980) (2)
Summing a polynomial function over integral points of a polygon. User's guide (2009) (2)
A Remark on the Convolution with Box Splines (2010) (2)
Quillen's relative Chern character (2009) (2)
Euler-MacLaurin formula for the multiplicities of the index of transversally elliptic operators (2012) (2)
Moment Cones of Representations (2014) (2)
Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology (1993) (1)
Cohomological Aspects of Hamiltonian Group Actions and Toric Varieties (2004) (1)
Equivariant Differential Forms (1992) (1)
Computation of the Highest Coefficients of Weighted Ehrhart Quasi-polynomials of Rational Polyhedra (2011) (1)
A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes (2011) (1)
ALL WHAT I WANTED TO KNOW ABOUT LANGLANDS PROGRAM AND WAS AFRAID TO ASK. (2006) (1)
Non commutative harmonic analysis and Lie groups : proceedings of the international conference held in Marseille Luminy, 21-26 June, 1982 (1983) (1)
The cocycle of the Shale-Weil representation and the Maslov index (1980) (1)
Top degree coefficients of the denumerant (2013) (1)
Non-commutative harmonic analysis : proceedings, Marseille-Luminy, France, June 26 to 30, 1978 : actes du Colloque d'analyse harmonique non commutative (1979) (1)
The Orbit Method in Representation Theory: Proceedings of a Conference Held in Copenhagen, August to September 1988 (1990) (1)
Highest coefficients of weighted Ehrhart quasi-polynomials for a rational polytope (2009) (1)
Semi-classical limits of geometric quantization and the graded equivariant Todd class (2018) (0)
Moment cone membership for quivers in strongly polynomial time (2023) (0)
Background on Differential Geometry (1992) (0)
Lecture 2 Residue Formulae For Volumes And Number Of Integral Points In Convex Rational Polytopes (2003) (0)
A ug 2 00 6 Applications of Equivariant Cohomology (2006) (0)
Formal equivariant $\widehat A$ class, splines and multiplicities of the index of transversally elliptic operators@@@Formal equivariant $\widehat A$ class, splines and multiplicities of the index of transversally elliptic operators (2016) (0)
Semi-classical analysis of piecewise quasi-polynomial functions and applications to geometric quantization (2019) (0)
1 7 Ju l 2 00 6 Applications of Equivariant Cohomology (2006) (0)
The Kirillov Formula for the Equivariant Index (1992) (0)
Arrangements of hyperplanes II: Szenes formula and Eisenstein series (1999) (0)
Cohen lifting of modular forms (1980) (0)
Zagier modular forms and the Doi-Naganuma correspondence (1980) (0)
The Family Index Theorem (1992) (0)
The Weyl transform and the Stone-Von Neumann theorem (1980) (0)
θ-Series Associated to Quadratic forms (1980) (0)
The Equivariant Index Theorem (1992) (0)
Irving Ezra Segal (1918–1998), Volume 46, Number 6 (1998) (0)
Index Density of Dirac Operators (1992) (0)
Lattices and representations of the Heisenberg group (1980) (0)
Non commutative harmonic analysis : actes du Colloque d'analyse harmonique non commutative, Marseille-Luminy, 1 au 5 juillet 1974 (1975) (0)
Laudatio of Bertram Kostant (2017) (0)
The Heisenberg group and the Schrödinger representation (1980) (0)
ADMISSIBLE COADJOINT ORBITS FOR COMPACT LIE GROUPS (2017) (0)
Non commutative harmonic analysis and Lie groups : actes du Colloque d'analyse harmonique non commutative, 16 au 20 juin 1980, Marseille-Luminy (1981) (0)
Symmetry and causality properties of physical fields ( wave equation / conformal group / fundamental particles ) (0)
Symplectic vector spaces and the Heisenberg Lie algebra (1980) (0)
Modular forms on the upper half-plane (1980) (0)
The Exponential Map and the Index Density (1992) (0)
short-circuit contact foldable and application of this short-circuit terminal in a photoelectric roehre (1987) (0)
Lattice reformulation of integer programming problems (2008) (0)
Geometric Quantization and Equivariant (2021) (0)
Lecture 1 Residue Formulae For Bernoulli Polynomials And Verlinde Sums (2003) (0)
Tensor product of holomorphic discrete series representations of U(p,q) and quivers (2023) (0)
Shifts of prepotentials (2022) (0)
retractable short circuit and use of the short circuit in a photoelectric tube (1986) (0)
The universal covering group of the symplectic group (1980) (0)
Fourier transforms and intertwining operators (1980) (0)
C O / 0 30 32 28 v 1 1 9 M ar 2 00 3 Counting Integer Flows in Networks (0)
Introduction. Let G be a compact Lie group acting by positive iso- metries on a compact oriented Riemannian manifold M of even dimen- sion. Let CV be a G equivariant Clifford module over M and let (2016) (0)
Geometric quantization in representation theory (2018) (0)
conjecture, the Mixed Toric Residue Mirror Conjecture (MTRMC), which (2004) (0)
Clifford Modules and Dirac Operators (1992) (0)
A pr 2 00 8 Index of transversally elliptic operators (2008) (0)
Q A ] 9 A ug 2 00 5 Covariant q-differential operators and unitary highest weight representations for U q su n , n (2005) (0)
Oriented Lagrangian planes and the metaplectic group (1980) (0)

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