A Variational Method for Functionals Depending on Eigenvalues

Explore a seminar on spectral geometry that delves into a new variational method for functionals depending on eigenvalues. Learn about optimization problems in spectral geometry involving eigenvalues associated with operators like the Laplacian or Dirichlet-to-Neumann on Riemannian manifolds. Discover how this approach has led to the construction of new minimal surfaces in recent years. Understand the challenges of working with functionals that are not C1 at metrics with eigenvalue multiplicity greater than 2, and how a subdifferential is used to generalize concepts of gradient, critical points, and Palais-Smale sequences. Examine the application of this new method in simplifying and unifying previous optimization results in dimension 2, as well as its generalization to higher dimensions. This 51-minute talk by Romain Petrides from Université Paris Diderot, presented at the Centre de recherches mathématiques (CRM), offers valuable insights into advanced mathematical techniques in spectral geometry.