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- Jean-Michel Bismut

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
44
Citations
10,269
155
World Ranking
1071
National Ranking
52

2004 - German National Academy of Sciences Leopoldina - Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften Mathematics

1998 - Member of Academia Europaea

1991 - Academie des sciences, France

1990 - Ampère Prize (Prix Ampère de l’Électricité de France), French Academy of Sciences

- Mathematical analysis
- Pure mathematics
- Topology

His primary areas of study are Pure mathematics, Algebra, Dirac operator, Analytic torsion and Flat vector bundle. His work is dedicated to discovering how Pure mathematics, Mathematical analysis are connected with Bundle and other disciplines. Jean-Michel Bismut has researched Algebra in several fields, including Pontryagin's minimum principle, Optimal control, Duality, Dirac and Chern class.

The Dirac operator study combines topics in areas such as Dirac algebra and Atiyah–Singer index theorem. He focuses mostly in the field of Analytic torsion, narrowing it down to matters related to Vector bundle and, in some cases, Holomorphic vector bundle and Holomorphic function. His Eta invariant research incorporates elements of Fiber, Invertible matrix, Base, Algebraic number and Adiabatic process.

- Conjugate convex functions in optimal stochastic control (570 citations)
- The analysis of elliptic families. II. Dirac operators, eta invariants, and the holonomy theorem (416 citations)
- Large Deviations and the Malliavin Calculus (371 citations)

Pure mathematics, Mathematical analysis, Hypoelliptic operator, Vector bundle and Analytic torsion are his primary areas of study. Much of his study explores Pure mathematics relationship to Algebra. His work deals with themes such as Boundary and Character, which intersect with Mathematical analysis.

His Hypoelliptic operator study which covers Laplace operator that intersects with Cotangent bundle. The various areas that he examines in his Vector bundle study include Cohomology, Chern class and Holomorphic vector bundle. His Analytic torsion study combines topics in areas such as Toeplitz matrix and Line bundle.

- Pure mathematics (50.00%)
- Mathematical analysis (31.17%)
- Hypoelliptic operator (19.48%)

- Pure mathematics (50.00%)
- Hypoelliptic operator (19.48%)
- Vector bundle (18.83%)

Jean-Michel Bismut mostly deals with Pure mathematics, Hypoelliptic operator, Vector bundle, Laplace operator and Mathematical analysis. Pure mathematics is closely attributed to Calculus in his research. His Hypoelliptic operator research is multidisciplinary, incorporating perspectives in Connection form, Cohomology, Riemann hypothesis, Heat kernel and Section.

His Vector bundle study also includes fields such as

- Holomorphic function, which have a strong connection to Dirac operator,
- Fibration which intersects with area such as Line bundle and Operator theory,
- Projection that intertwine with fields like Chern class and Character. Jean-Michel Bismut has included themes like Harmonic analysis, Clifford algebra, Limit and Rotation in his Laplace operator study. Jean-Michel Bismut interconnects Adiabatic process, Connection and Mathematical physics in the investigation of issues within Mathematical analysis.

- Hypoelliptic Laplacian and Orbital Integrals (42 citations)
- Hypoelliptic Laplacian and Bott–Chern Cohomology (19 citations)
- ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS (17 citations)

- Mathematical analysis
- Pure mathematics
- Geometry

His primary areas of investigation include Pure mathematics, Laplace operator, Hypoelliptic operator, Mathematical analysis and Vector bundle. Many of his research projects under Pure mathematics are closely connected to Index with Index, tying the diverse disciplines of science together. His Cohomology research is multidisciplinary, relying on both Holomorphic function and Limit.

The concepts of his Laplace operator study are interwoven with issues in Connection and Riemann surface. In the field of Mathematical analysis, his study on Tangent bundle, Measure and Riemannian manifold overlaps with subjects such as Geometric Brownian motion. As a part of the same scientific family, Jean-Michel Bismut mostly works in the field of Vector bundle, focusing on Analytic torsion and, on occasion, Operator theory, Differential form and Asymptotic expansion.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Conjugate convex functions in optimal stochastic control

Jean-Michel Bismut.

Journal of Mathematical Analysis and Applications **(1973)**

927 Citations

Large Deviations and the Malliavin Calculus

Jean-Michel Bismut.

**(1984)**

592 Citations

An Introductory Approach to Duality in Optimal Stochastic Control

Jean-Michel Bismut.

Siam Review **(1978)**

555 Citations

The analysis of elliptic families. II. Dirac operators, eta invariants, and the holonomy theorem

Jean Michel Bismut;Daniel S Freed.

Communications in Mathematical Physics **(1986)**

429 Citations

The analysis of elliptic families. I. Metrics and connections on determinant bundles

Jean Michel Bismut;Daniel S Freed.

Communications in Mathematical Physics **(1986)**

424 Citations

The Atiyah-Singer index theorem for families of Dirac operators: two heat equation proofs

Jean-Michel Bismut.

Inventiones Mathematicae **(1986)**

420 Citations

A local index theorem for non Kähler manifolds

Jean-Michel Bismut.

Mathematische Annalen **(1989)**

413 Citations

Analytic torsion and holomorphic determinant bundles I. Bott-Chern forms and analytic torsion

J. M. Bismut;H. Gillet;C. Soulé.

Communications in Mathematical Physics **(1988)**

370 Citations

Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions

Jean Michel Bismut.

Probability Theory and Related Fields **(1981)**

369 Citations

Linear Quadratic Optimal Stochastic Control with Random Coefficients

Jean-Michel Bismut.

Siam Journal on Control and Optimization **(1976)**

356 Citations

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