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- Cédric Villani

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
48
Citations
22,498
124
World Ranking
859
National Ranking
43

2013 - Academie des sciences, France

2012 - Member of Academia Europaea

2010 - Fields Medal of International Mathematical Union (IMU) For his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation.

- Mathematical analysis
- Geometry
- Algebra

Cédric Villani mostly deals with Mathematical analysis, Statistical physics, Kinetic theory of gases, Sobolev inequality and Boltzmann equation. His study on Mathematical analysis is mostly dedicated to connecting different topics, such as Pure mathematics. Cédric Villani has included themes like Euclidean structure and Norm in his Pure mathematics study.

His Sobolev inequality research incorporates themes from Kantorovich inequality, Rearrangement inequality, Log sum inequality, Interpolation inequality and Logarithm. His research combines Boltzmann constant and Boltzmann equation. Cédric Villani works mostly in the field of Smoothness, limiting it down to topics relating to Infinity and, in certain cases, Cauchy problem.

- Topics in Optimal Transportation (2889 citations)
- Optimal Transport: Old and New (2755 citations)
- Ricci curvature for metric-measure spaces via optimal transport (1049 citations)

His primary areas of study are Mathematical analysis, Boltzmann equation, Pure mathematics, Ricci curvature and Sobolev inequality. He conducted interdisciplinary study in his works that combined Mathematical analysis and Homogeneous. The Boltzmann equation study combines topics in areas such as Entropy production, Statistical physics, Boltzmann constant and Mathematical physics.

His research integrates issues of Poincaré inequality, Geodesic and Space in his study of Pure mathematics. His Poincaré inequality research incorporates elements of Kantorovich inequality and Rearrangement inequality. His Ricci curvature study which covers Scalar curvature that intersects with Riemann curvature tensor.

- Mathematical analysis (45.45%)
- Boltzmann equation (21.97%)
- Pure mathematics (16.67%)

- Mathematical analysis (45.45%)
- Curvature (10.61%)
- Ricci curvature (13.64%)

Mathematical analysis, Curvature, Ricci curvature, Boltzmann equation and Mathematics education are his primary areas of study. His is doing research in Fourier transform, Limit, Riemannian geometry, Monotonic function and Bounded function, both of which are found in Mathematical analysis. His Riemannian geometry study integrates concerns from other disciplines, such as Fundamental theorem of Riemannian geometry, Wasserstein metric, Topology, Geodesic convexity and Riemannian surface.

Cédric Villani interconnects Duality, Riemann curvature tensor, Hypercube, Jacobian matrix and determinant and Scalar curvature in the investigation of issues within Ricci curvature. His Boltzmann equation research is multidisciplinary, relying on both Entropy production, Vlasov equation, Boltzmann constant and Mathematical physics. His Entropy production research integrates issues from Entropy, Sobolev inequality, Spectral gap and Conjecture.

- Optimal Transport: Old and New (2755 citations)
- On Landau damping (332 citations)
- Entropy and chaos in the Kac model (71 citations)

- Mathematical analysis
- Geometry
- Algebra

The scientist’s investigation covers issues in Mathematical analysis, Curvature, Riemann curvature tensor, Ricci curvature and Riemannian geometry. His study connects Landau damping and Mathematical analysis. Cédric Villani combines subjects such as Corollary and Regular polygon with his study of Curvature.

His research in Riemann curvature tensor intersects with topics in Scalar curvature and Combinatorics. His Ricci curvature research includes themes of Geodesic convexity, Jacobian matrix and determinant, Wasserstein metric and Duality. His Riemannian geometry study combines topics in areas such as Exponential map, Fundamental theorem of Riemannian geometry and Monotonic function, Topology.

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.

Optimal Transport: Old and New

Cédric Villani.

**(2013)**

5222 Citations

Topics in Optimal Transportation

Cédric Villani.

**(2003)**

5128 Citations

Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

F. Otto;C. Villani.

Journal of Functional Analysis **(2000)**

1369 Citations

Ricci curvature for metric-measure spaces via optimal transport

John Lott;Cedric Villani.

Annals of Mathematics **(2009)**

1188 Citations

Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory

Cédric Villani.

Handbook of Mathematical Fluid Dynamics **(2002)**

1112 Citations

On Landau damping

Clément Mouhot;Cédric Villani.

Acta Mathematica **(2011)**

537 Citations

On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation

L. Desvillettes;C. Villani.

Inventiones Mathematicae **(2005)**

529 Citations

On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations

Cédric Villani.

Archive for Rational Mechanics and Analysis **(1998)**

526 Citations

Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates

José A. Carrillo;Robert J. McCann;Cédric Villani.

Revista Matematica Iberoamericana **(2003)**

498 Citations

Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media

José A. Carrillo;Robert J. McCann;Cédric Villani.

Archive for Rational Mechanics and Analysis **(2006)**

380 Citations

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