Differential Geometry Seminar: Spectra of hyperbolic three-manifolds

Speaker: Francesco Lin (Columbia University)

Title: Spectra of hyperbolic three-manifolds

Abstract: A fundamental problem at the interface of differential geometry and analysis of PDEs is to understand the spectra of natural differential operators on a given Riemannian manifold. In this talk, motivated by the question of understanding topological invariants of three-manifolds arising from Floer theory, I will focus on the problem of understanding the spectra of the Hodge and Dirac operators on compact hyperbolic three-manifolds. In particular, I will discuss how these can be explicitly studied in concrete examples via the Selberg trace formula using ideas from Fourier optimization, taking as input computations in hyperbolic geometry. This is joint work with M. Lipnowski.