Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds


From September 1 to December 12, the Institut Henri Poincare will organize a thematic semester: Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds.

I look forward to this event. I will be in sabbatical this Fall and it will be the occasion for me to spend two months in Paris participating to the exciting activities of the trimester.

At the beginning of September, I will deliver a 12h course on hypoelliptic diffusion operators. The lectures will be published on this blog.

Sub-Laplacians and Hypoelliptic operators on Riemannian foliations

  • Riemannian foliations with totally geodesic fibers and their Laplacians
  • Examples of¬†Riemannian foliations and their sub-Laplacians: The Hopf fibrations
  • Weitzenbock formulas for the horizontal Laplacian
  • First eigenvalue estimates
  • The horizontal heat semigroup
  • The horizontal Bonnet-Myers theorem
  • Applications of Riemannian foliations to Fokker-Planck type kinetic equations
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