Extracting Hadamard coefficients from Green’s expansions

19.10.2023, 16:00  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Lennart Ronge (UP)

Hadamard coefficients are a Lorentzian equivalent to the Riemannian heat kernel coefficients. They encode information about the geometry of the underlying Lorentzian manifold (e.g. the scalar curvature) and the associated differential operators (e.g. the index density). The Hadamard coefficients also occur in an asymptotic expansion for the kernels of Green’s operators. We "invert" this expansion to obtain a formula for the (diagonal values of) Hadamard coefficients in terms of Green’s operators (or more precisely a Green’s operator analogue of a resolvent).