The APDE seminar on Monday, 4/28, will be given by Kiril Datchev (Purdue University) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PDT. To participate, please email Robert Schippa (rschippa@berkeley.edu).

Title: Low frequency scattering and decay of waves.

Abstract: Low frequency waves are sensitive to the large-scale geometry of the environment through which they travel and of scatterers with which they interact. Their analysis has implications for wave evolution, and for the scattering matrix and phase. We study these using resolvent asymptotics, and present a robust method for deriving such asymptotics, based in part on an identity of Vodev and on boundary pairing. We focus on two-dimensional Euclidean scattering because of the rich phenomena observed in this setting, but other dimensions work just as well, and the method also applies to more general geometric situations.

This project is joint work with Tanya Christiansen, and parts are also joint work with Colton Griffin, Pedro Morales, and Mengxuan Yang.