Low energy resolvent expansions in dimension two

We prove resolvent expansions near zero energy for compactly supportedperturbations of the Laplacian on $\mathbb R^2$. We obtain precise results forgeneral self-adjoint black box perturbations, in the sense of Sj\"ostrand andZworski, and also for some non-self-adjoint ones. We compute the most singularterms, relating them to spaces of zero eigenvalues and resonances. Our methodsinclude resolvent identity arguments following Vodev and boundary pairingarguments following Melrose.