Jean-Michel Bismut

Jean-Michel Bismut's AcademicInfluence.com Rankings

Jean-Michel Bismut

Mathematics

#398

World Rank

#806

Historical Rank

Measure Theory

#1249

World Rank

#1585

Historical Rank

mathematics Degrees

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Mathematics

Why Is Jean-Michel Bismut Influential?

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According to Wikipedia, Jean-Michel Bismut is a French mathematician who has been a professor at the Université Paris-Sud since 1981. His mathematical career covers two apparently different branches of mathematics: probability theory and differential geometry. Ideas from probability play an important role in his works on geometry.

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Jean-Michel Bismut'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

Conjugate convex functions in optimal stochastic control (1973) (693)
Large Deviations and the Malliavin Calculus (1984) (496)
An Introductory Approach to Duality in Optimal Stochastic Control (1978) (422)
The analysis of elliptic families (1986) (391)
A local index theorem for non Kähler manifolds (1989) (324)
Analytic torsion and holomorphic determinant bundles (1988) (320)
An extension of a theorem by Cheeger and Müller (1992) (311)
The analysis of elliptic families. I. Metrics and connections on determinant bundles (1986) (291)
Linear Quadratic Optimal Stochastic Control with Random Coefficients (1976) (290)
The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs (1986) (275)
Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions (1981) (264)
Analytic torsion and holomorphic determinant bundles I. Bott-Chern forms and analytic torsion (1988) (260)
Complex immersions and Quillen metrics (1991) (234)
Eta invariants and their adiabatic limits (1989) (189)
Flat vector bundles, direct images and higher real analytic torsion (1995) (177)
The Atiyah—Singer theorems: A probabilistic approach. I. The index theorem (1984) (136)
Analytic torsion and holomorphic determinant bundles. II: Direct images and Bott-Chern forms (1988) (123)
Localization formulas, superconnections, and the index theorem for families (1986) (109)
Index theorem and equivariant cohomology on the loop space (1985) (109)
Analytic Torsion and Holomorphic Determinant Bundles II (2004) (105)
The Atiyah-Singer theorems: A probabilistic approach. II. The Lefschetz fixed point formulas (1984) (104)
Milnor and ray-singer metrics on the equivariant determinant of a flat vector bundle (1994) (95)
The Witten complex and the degenerate Morse inequalities (1986) (92)
The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle (1989) (92)
Families index for manifolds with boundary, superconnections, and cones. I, Families of manifolds with boundary and Dirac operators (1990) (87)
Equivariant immersions and Quillen metrics (1995) (83)
A generalized formula of Ito and some other properties of stochastic flows (1981) (83)
The hypoelliptic Laplacian on the cotangent bundle (2005) (81)
Growth and optimal intertemporal allocation of risks (1975) (80)
Analytic torsion and holomorphic determinant bundles (1988) (72)
Families index for manifolds with boundary, superconnections and cones. II. The Chern character (1990) (68)
Demailly's asymptotic Morse inequalities: A heat equation proof (1987) (61)
Hypoelliptic Laplacian and Orbital Integrals (2011) (56)
Families Torsion and Morse Functions (2002) (56)
Superconnection currents and complex immersions (1990) (55)
The hypoelliptic Laplacian and Ray-Singer metrics (2008) (51)
Holomorphic families of immersions and higher analytic torsion forms (1997) (48)
Bott-Chern currents and complex immersions (1990) (44)
Remarks on the index theorem for families of Dirac operators on manifolds with boundary (1990) (43)
An example of interaction between information and control (1973) (41)
Quillen metrics and higher analytic torsion forms. (1994) (40)
Symplectic geometry and the Verlinde Formulas (1999) (38)
The infinitesimal Lefschetz formulas: A heat equation proof (1985) (38)
Real embeddings and eta invariants (1993) (36)
Complex Immersions and Arakelov Geometry (2007) (34)
Equivariant de Rham torsions (2004) (33)
Last exit decompositions and regularity at the boundary of transition probabilities (1985) (32)
ETA INVARIANTS, DIFFERENTIAL CHARACTERS AND FLAT VECTOR BUNDLES (2005) (30)
Index Theorem and the Heat Equation (2010) (30)
Martingales, the Malliavin calculus and Hörmander's theorem (1981) (29)
Koszul complexes, harmonic oscillators, and the Todd class (1990) (28)
Hypoelliptic Laplacian and Bott–Chern Cohomology (2013) (28)
On Optimal Control of Linear Stochastic Equations with a Linear-Quadratic Criterion (1977) (27)
Holomorphic equivariant analytic torsions (2000) (26)
Partially Observed Diffusions and Their Control (1982) (26)
Equivariant short exact sequences of vector bundles and their analytic torsion forms (1994) (25)
ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS (2015) (24)
Transgressed Euler classes of ${\rm SL}(2n,\mathbf{Z})$ vector bundles, adiabatic limits of eta invariants and special values of $L$-functions (1992) (22)
Hypoelliptic Laplacian and probability (2015) (21)
The calculus of boundary processes (1984) (21)
Equivariant Bott-Chern currents and the Ray-Singer analytic torsion (1990) (21)
Holomorphic immersions and equivariant torsion forms (2004) (21)
Local Index Theory, Eta Invariants and Holomorphic Torsion: a survey (1996) (20)
The hypoelliptic Laplacian on a compact Lie group (2008) (17)
Hypoelliptic Laplacian and Bott-Chern Cohomology: A Theorem of Riemann-Roch-Grothendieck in Complex Geometry (2013) (17)
Duality Methods in the Control of Densities (1978) (16)
Probability and geometry (1986) (13)
The Hypoelliptic Dirac Operator (2007) (13)
Loop Spaces and the hypoelliptic Laplacian (2008) (12)
Duistermaat-Heckman formulas and index theory (2011) (12)
Holomorphic and de Rham torsion (2004) (12)
Control of jump processes and applications (1978) (12)
Torus bundles and the group cohomology of GL(N,Z) (1995) (11)
An introduction to the stochastic calculus of variations (1982) (11)
Complex equivariant intersection, excess normal bundles and Bott-Chern currents (1992) (11)
The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle (1990) (10)
An Example of Optimal Stochastic Control with Constraints (1974) (10)
The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167) (2008) (10)
Hypoelliptic Laplacian and Orbital Integrals (AM-177) (2011) (9)
Index Theory and the Hypoelliptic Laplacian (2012) (8)
Laplacien hypoelliptique et torsion analytique (2005) (7)
On certain infinite dimensional aspects of Arakelov intersection theory (1992) (7)
Bott-Chern currents, excess normal bundles and the Chern character (1992) (7)
A survey of the hypoelliptic Laplacian (2009) (7)
Eta invariants and the hypoelliptic Laplacian (2016) (7)
Jump Processes and Boundary Processes (1984) (7)
An inequality for processes which satisfy Kolmogorov's continuity criterion. Application to continuous martingales (1983) (7)
Transgressed Chern forms for Dirac operators (1988) (6)
An Approximation Method in Optimal Stochastic Control (1978) (6)
Probability Theory Methods in Zero-Sum Stochastic Games (1977) (5)
Eta invariants and complex immersions (1990) (5)
On the set of zeros of certain semi-martingales (1984) (5)
Convex inequalities in stochastic control (1981) (5)
Fibrés plats, images directes et formes de torsion analytique (1993) (5)
The index theorem for families of Dirac operators on manifolds with boundary; susperconnections and cones; II (1990) (3)
An introduction to duality in random mechanics (1979) (3)
Potential theory in optimal stopping and alternatinc processes (1979) (3)
Coherent sheaves, superconnections, and RRG (2021) (3)
Geometric orbital integrals and the center of the enveloping algebra (2019) (3)
The hypoelliptic Laplacian and Chern-Gauss-Bonnet (2006) (2)
The hypoelliptic Laplacian (2017) (2)
Eta-invariants and families index for manifolds with boundary (1987) (1)
Toeplitz Operators, Analytic Torsion, and the Hypoelliptic Laplacian (2016) (1)
Torus bundles and the group cohomology of ${\rm GL}(N,\bold Z)$ (1997) (1)
Chapter Fourteen. The heat kernel qXb;t for bounded b (2011) (0)
Chapter Seven. An application to local index theory (2011) (0)
The holomorphic adiabatic limit (2013) (0)
Exotic superconnections and Riemann-Roch-Grothendieck (2013) (0)
Chapter 5. The limit as t → +∞ and b → 0 of the superconnection forms (2008) (0)
Chapter 6. Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics (2008) (0)
Chapter Thirteen. Refined estimates on the scalar heat kernel for bounded b (2011) (0)
Proprétés d’intersection du flot ϕ.(ω,.) (1981) (0)
Chapter 17. The limit of A'2φb,±H as b → 0 (2008) (0)
Isadore M. Singer (1924–2021) In Memoriam Part 1: Scientific Works (2022) (0)
Chapter 11. A proof of equation (8.4.6) (2008) (0)
Chapter Four. Elliptic and hypoelliptic orbital integrals (2011) (0)
The hypoelliptic superconnection forms (2013) (0)
Media Metrics Downloaded : 15 Viewed : 0 Size : 1 . 46 MB Type : application (2019) (0)
Chapter Ten. The action functional and the harmonic oscillator (2011) (0)
Chapter 12. A proof of equation (8.4.8) (2008) (0)
The hypoelliptic superconnection forms when {\bar\partial}^{M} {\partial^{M}} \omega^{M} = 0 (2013) (0)
Chapter Twelve. Rough estimates on the scalar heat kernel (2011) (0)
The elliptic superconnections (2013) (0)
Chapter 9. A comparison formula for the Ray-Singer metrics (2008) (0)
Chapter 15. The hypoelliptic estimates (2008) (0)
Chapter 7. The hypoelliptic torsion forms of a vector bundle (2008) (0)
Chapter 2. The hypoelliptic Laplacian on the cotangent bundle (2008) (0)
Chapter 8. Hypoelliptic and elliptic torsions: a comparison formula (2008) (0)
Chapter 14. The integration by parts formula (2008) (0)
Chapter 10. The harmonic forms for b → 0 and the formal Hodge theorem (2008) (0)
Chapter Fifteen. The heat kernel qXb;t for b large (2011) (0)
The Riemannian adiabatic limit (2013) (0)
The hypoelliptic superconnections (2013) (0)
Chapter Two. The hypoelliptic Laplacian on X = G/K (2011) (0)
Chapter Eight. The case where [k (γ) ; p0] = 0 (2011) (0)
Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel (2008) (0)
Chapter Three. The displacement function and the return map (2011) (0)
Chapter Six. A formula for semisimple orbital integrals (2011) (0)
Chapter Five. Evaluation of supertraces for a model operator (2011) (0)
Chapter Nine. A proof of the main identity (2011) (0)
Chapter 1. Elliptic Riemann-Roch-Grothendieck and flat vector bundles (2008) (0)
Chapter 4. Hypoelliptic Laplacians and odd Chern forms (2008) (0)
Toeplitz Operators, Analytic Torsion, and the Hypoelliptic Laplacian (2016) (0)
Index of Notation (2008) (0)
Chapter 13. A proof of equation (8.4.7) (2008) (0)
Chapter 16. Harmonic oscillator and the J0 function (2008) (0)
On hypoelliptic bridge* (2016) (0)
The elliptic superconnection forms (2013) (0)
Chapter Eleven. The analysis of the hypoelliptic Laplacian (2011) (0)
The exotic superconnection forms of a vector bundle (2013) (0)
Chapter One. Clifford and Heisenberg algebras (2011) (0)
The hypoelliptic superconnection forms of vector bundles (2013) (0)

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