This talk will focus on low-energy resolvent expansions for a wide class of scattering settings.  We concentrate on operators acting on \(\mathbb{R}^2\), with particular attention to the Dirichlet or Neumann Laplacian on the exterior of an obstacle and to Aharonov-Bohm operators.  We give applications to long-time behavior of the solutions of the wave equation and low-energy behavior of the scattering phase.

This is based on joint work with Kiril Datchev.  A portion is also with Mengxuan Yang and Pedro Morales.