Raphael Ponge (March 9th)

Speaker: Raphael Ponge (UC Berkeley / Seoul National University)

Title: On the singularities of the Green functions of the conformal powers of the Laplacian.

Abstract: Green functions play a major role in PDEs and conformal geometry. In this talk, I will explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. This includes the Yamabe and Paneitz operators, as well as the conformal fractional powers originating from the work of Graham-Zworski on scattering theory for AH metrics. The results are formulated in terms of explicit conformal invariants arising from the ambient Lorentzian metric of Fefferman-Graham. As applications we obtain a new characterization of locally conformally flat manifolds and a spectral-theoretic characterization of the conformal class of the round sphere.