Spectral data of the Kohn Laplacian on sphere quotients is rich, structured, and explicitly computable—yet its geometric implications are not always transparent. In this expository talk, I will revisit earlier work on computing spectra of the Kohn Laplacian on spheres and lens spaces, emphasizing how symmetry and group actions shape eigenvalues and multiplicities. I will then outline a new direction: using machine learning tools to identify patterns and invariants in these spectra, with the aim of better understanding how geometry, arithmetic, and symmetry are reflected in spectral signatures. This perspective positions AI as a hypothesis-generating tool for classical problems in analysis and geometry.
