BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michał Wrochna ((Université de Cergy-Pontoise) DTSTART:20210409T121500Z DTEND:20210409T131500Z DTSTAMP:20260423T010753Z UID:EXACT/1 DESCRIPTION:Title: Sp ectral actions on asymptotically Minkowski spacetimes\nby Michał Wroc hna ((Université de Cergy-Pontoise) as part of EXACT - (KRAKOW - POZNAN - WARSAW) Field Theory\n\n\nAbstract\nThe spectral theory of the Laplace– Beltrami operator on Riemannian manifolds is known to be intimately relate d to geometric invariants such as the Einstein-Hilbert action. These relat ionships have inspired many developments in physics including the Chamsedd ine–Connes action principle in the non-commutative geometry programme. H owever\, a priori they do only apply to the case of Euclidean signature. T he physical setting of Lorentzian manifolds has in fact remained largely p roblematic: elliptic theory no longer applies and something different is n eeded.\n\nIn this talk I will report on joint work on this problem with Ng uyen Viet Dang. We consider perturbations of Minkowski space and more gene ral spacetimes on which the d’Alembertian P is essentially self-adjoint (thanks to recent results by Dereziński–Siemssen\, Vasy and Nakamura– Taira). It is then possible to define functions of P\, and we demonstrate that their Schwartz kernels have geometric content largely analogous to th e Riemannian setting. In particular\, we define a Lorentzian spectral zeta function and relate one of its poles to the Einstein–Hilbert action\, p aralleling thus a result in Euclidian signature attributed to Connes\, Kas tler and Kalau–Walze.\n\nThe primary consequence is that gravity can be obtained from a spectral action directly in Lorentzian signature. The proo fs involve mathematical ingredients from Quantum Field Theory on curved sp acetime\, in particular the Feynman propagator.\n\nPlease contact the orga nizers for the link to the meeting.\n LOCATION:https://researchseminars.org/talk/EXACT/1/ END:VEVENT END:VCALENDAR