Title: Low frequency scattering asymptotics in dimension two
Speaker: Kiril Datchev
Speaker Info: Purdue
Two-dimensional scattering theory comes with special challenges due to singularities which appear at low frequencies. I will present a new technique, which is elementary and robust, for dealing with these singularities, focusing on the fundamental example of obstacle scattering, where the leading singularities are given in terms of the obstacle's logarithmic capacity or Robin constant. The technique is based on a resolvent identity of Vodev.Date: Monday, February 13, 2023
We expect similar results to hold for more general scattering problems, including singular magnetic vector potentials, corresponding to the Aharonov--Bohm effect in quantum mechanics. This talk is based on joint work with Tanya Christiansen, and joint work in progress with Tanya Christiansen and Mengxuan Yang.