Orthogonal polynomials and an exotic disk geometry arising from the one-dimensional wave equation
Expositor: Peter Gibson
Instituição: York U
Data e Horário: 17/12/2019 | 17:00 hs
Resumo: The one-dimensional wave equation models sound propagation in layered media such as sedimentary geological formations, layered biological tissues like skin or the retina, or laminated structures in the built environment. Acoustic imaging of layered media is a practical application that has driven research on inverse scattering for the one-dimensional wave equation since the mid twentieth century. Recent work has revealed some unexpected mathematical connections to orthogonal polynomials (in two flavours) as well as an exotic Riemannian structure on the disk. These new connections illuminate the inverse scattering problem and underly a fast, accurate inversion algorithm that allows one to recover acoustic impedance as a function of spatial location from echoes measured at a fixed location.