Programme

Antoine Henrot (U. de Lorraine) Isoperimetric inequalities for eigenvalues. This course will give an overview of the classical isoperimetric inequalities satisfied by the eigenvalues of the Laplacian with Dirichlet boundary conditions in the Euclidean case. Some important tools of modern analysis will be presented, such as symmetrization and rearrangement, Hausdorff convergence, γ-convergence, and shape derivative. A number of open problems will be also discussed.

Jimmy Lamboley (U. Paris-Dauphine) Shape optimization under convexity constraint. The course will focus on recent advances in shape optimization under convexity constraint of various functionals involving analytic and geometric data, such as the Dirichlet eigenvalues, the Mahler volume and the p-torsion.

Ailana Fraser (UBC) Minimal surfaces and extremal eigenvalue problems on surfaces. Maximizing Laplace eigenvalues on a given Riemannian surface under the area constraint is a fundamental problem in spectral geometry. There has been a number of important recent developments on the subjects, such as the existence and regularity results for maximizing metrics on surfaces, as well as the development of the theory of extremal metrics for Steklov eigenvalues. It turns out that minimal surfaces play a key role in the study of extremal metrics for both Laplace and Steklov eigenvalues. The minicourse will emphasize this connection, wth the focus on recent results of Fraser and Schoen on extremal problems for Steklov eigenvalues.

Alessandro Savo (U. di Roma) Overdetermined PDEs in Riemannian geometry. The minicourse will focus on various important overdetermined problems for geometric PDEs, such as the Pompeiu problem, the Schiffer conjecture, the Serrin problem - both in the Euclidean and the Riemannian settings, as well as some overdetermined problems arising in the study of the heat diffusion. Connections to minimal surfaces and the Steklov problem will be also discussed.

Almut Burchard (U. Toronto) Symmetrization methods and sharp geometric inequalities. Syllabus TBA.

Lundi

  • 9:00-10:30 == A. Henrot
  • 10:30-11:00 == Pause
  • 11:00-12:30 == A. Burchard
  • 12:30-14:00 == Lunch
  • 14:00-15:00 == A. Savo
  • 15:00-15:30 == Pause café
  • 15:30-17:00 == Séance d’exercices

Mardi

  • 9:00-10:30 == A. Burchard
  • 10:30-11:00 == Pause
  • 11:00-12:30 == A. Savo
  • 12:30-14:00 == Lunch
  • 14:00-15:00 == A. Henrot
  • 15:00-15:30 == Pause café
  • 15:30-17:00 == Séance d’exercices

Mercredi

  • 9:00-10:30 == A. Savo
  • 10:30-11:00 == Pause
  • 11:00-12:30 == A. Fraser
  • 12:30-14:00 == Lunch
  • 14:00-15:00 == J. Lamboley
  • 15:00-15:30 == Pause café
  • 15:30-17:00 == Séance d’exercices

Jeudi

  • 9:00-10:30 == A. Fraser
  • 10:30-11:00 == Pause
  • 11:00-12:30 == J. Lamboley
  • 12:30-14:00 == Lunch
  • 14:00-15:00 == A. Burchard
  • 15:00-15:30 == Pause café
  • 15:30-17:00 == Séance d’exercices

Vendredi

  • 9:00-10:30 == J. Lamboley
  • 10:30-11:00 == Pause
  • 11:00-12:30 == A. Henrot
  • 12:30-14:00 == Lunch
  • 14:00-15:00 == A. Fraser
  • 15:00-15:30 == Séance d’exercices