On the Spectrum of the Poincaré Operator in Ellipsoids

Explore a 56-minute seminar from the Spectral Geometry in the clouds series, delivered by Yves Colin de Verdière on September 25, 2023. Delve into the intricacies of the Poincaré equation and its associated wave operator, known as the "Poincaré operator," as applied to ellipsoids. Discover a conceptual proof demonstrating the pure point spectrum with polynomial eigenfields in ellipsoidal domains, a phenomenon observed by physicists. Gain insights into the asymptotic behavior of eigenvalues and enhance your understanding of incompressible fluid motion in rotating domains. This mathematical exploration, organized by the Centre de recherches mathématiques (CRM), offers a deep dive into advanced concepts in spectral geometry and fluid dynamics.