Seminario

Seminario EDPs y Mecánica de Fluidos

Lorentzian spectral zeta functions

Ponente:  Michal Wrochna (Paris-Cergy)
Fecha:  jueves 13 de octubre de 2022 - 11:30
Lugar:  Aula Naranja, ICMAT

Resumen:

The spectral theory of the Laplace–Beltrami operator on Riemannian manifolds is known to be intimately related to geometric invariants. This kind of relationships has inspired many developments in relativistic physics, but a priori it only applies to the case of Euclidean signature. In contrast, the physical setting of Lorentzian manifolds has remained problematic for very fundamental reasons.

In this talk I will present results that demonstrate that there is a well-posed Lorentzian spectral theory nevertheless, and moreover, it is related to Lorentzian geometry in a way that has striking analogies with the Euclidean case. In particular, we show that the scalar curvature can be obtained as the pole of a spectral zeta function. The proof indicates that a key role is played by the dynamics of the null geodesic flow and its asymptotic properties. 

The talk is based on joint works with Nguyen Viet Dang (Jussieu) and András Vasy (Stanford).