Title: Zeta function of the wave operator on Lorentzian scattering spaces
Speaker: Michal Wrochna
Speaker Info: Cergy Paris
The spectral theory of the Laplace–Beltrami operator on Riemannian manifolds is known to be intimately related to geometric invariants thanks to e.g. zeta functions and heat kernel expansions. On the other hand, despite strong motivation from physics, the case of Lorentzian manifolds has remained mysterious: elliptic theory no longer applies so something different is needed.Date: Monday, January 11, 2021
In this talk I will report on joint work on this problem with Nguyen Viet Dang (Lyon). We consider the class of non-trapping Lorentzian scattering spaces, on which the wave operator P is known to be essentially self-adjoint by a recent result of Vasy. Complex powers of P are defined by functional calculus, and we show that their trace density exists as a meromorphic function. We relate the poles to geometric quantities including the scalar curvature, proving therefore a Lorentzian analogue of a theorem due to Connes, Kastler and Kalau–Walze.