What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- Topics in Optimal Transportation (2889 citations)
- Optimal Transport: Old and New (2755 citations)
- Ricci curvature for metric-measure spaces via optimal transport (1049 citations)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Mathematical analysis (45.45%)
- Boltzmann equation (21.97%)
- Pure mathematics (16.67%)
What were the highlights of his more recent work (between 2009-2018)?
- Mathematical analysis (45.45%)
- Curvature (10.61%)
- Ricci curvature (13.64%)
In recent papers he was focusing on the following fields of study:
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.
Between 2009 and 2018, his most popular works were:
- Optimal Transport: Old and New (2755 citations)
- On Landau damping (332 citations)
- Entropy and chaos in the Kac model (71 citations)
In his most recent research, the most cited papers focused on:
- 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.
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