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 length (in a sense that will be explained), and causal propagator eigenvalue. 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. My talk will be based on: https://arxiv.org/abs/2606.00311.

Bio: Joshua Jones is a PhD student at the Dublin Institute for Advanced Studies, supervised by Yasaman Yazdi. He did his undergraduate studies at Imperial College London, and a masters at the University of Cambridge. His interests are largely focused on entropy, black hole thermodynamics, and causal set theory. In particular, he studies entanglement entropy in the causal set as a potential source of the Bekenstein-Hawking entropy, championing a spacetime approach to the calculation such that one can regularise covariantly. One such regularisation is via the spectrum of the causal propagator, which is connected to Lorentzian spectral geometry.0311.