From Gas Giant Planets to the Spectral Theory of Subelliptic Laplacians

Explore a mathematical lecture that bridges planetary science and spectral theory, focusing on sound wave propagation in gas giant planets and its connection to sub-Riemannian geometry. Delve into collaborative research with Yves Colin de Verdière, Charlotte Dietze, and Maarten De Hoop examining how the unique properties of gas giants, where sound speed diminishes at the surface, relate to Riemannian manifolds with boundary metrics. Learn how variable transformations reduce Laplacian-Beltrami analysis to sub-Riemannian Laplacian study, with particular emphasis on calculating Weyl's law. Recorded during the "Frontiers in Sub-Riemannian Geometry" conference at the Centre International de Rencontres Mathématiques in Marseille, France, this hour-long presentation offers deep insights into the intersection of planetary physics and advanced mathematical theory.