Fields Seminar in Applied Math

Lorentzian spectral geometry, as a field, has enjoyed much less progress than its Riemannian counterpart. I will suggest that the causal propagator (the difference between the retarded and advanced Green functions) is the appropriate operator to be spectrally considered on Lorentzian manifolds. I will present a conjecture that connects null geodesic lengths (in a sense that will be explained), and the eigenvalues of the causal propagator. This gives the leading term in the asymptotic scaling of the spectral density, in analogy with Weyl's law for the Laplace-Beltrami operator. This opens many avenues for work in Lorentzian spectral geometry. It will be based on: https://arxiv.org/abs/2606.00311.

Joshua Jones is a doctoral student at the Dublin Institute for Advanced Study School of Theoretical Physics