Speaker: Alexandre Girouard (Université Laval)

Title: Symmetry Breaking and Hidden Symmetries in Eigenvalue Optimization

Abstract: In classical shape optimization, maximizers are often highly symmetric. This goes all the way back to the classical isoperimetric inequality, where balls uniquely maximize the volume under perimeter constraint. In this talk, I will explore the symmetries of shapes that optimize eigenvalues of Laplace and Dirichlet-to-Neumann operators under various geometric constraints. While these optimizers tend to exhibit symmetry, there are interesting exceptions where symmetries appear to be broken. But are they truly broken—or might they be subtly hidden, waiting to be uncovered a different perspective?