The University of Arizona
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Inverse Scattering: New answers to some old questions

Mathematics Colloquium

Inverse Scattering: New answers to some old questions
Series: Mathematics Colloquium
Location: ZOOM
Presenter: Fioralba Cakoni, Rutgers University
Abstract: From Rayleigh's explanation of why the sky is blue, to Rutherford's discovery of the atomic nucleus, through modern applications of computerized tomography and imaging, scattering theory has played a central role in 20th century mathematical physics and continues to be an important area of mathematics.  Although the basic mathematical model of direct scattering theory is deceptively simple, scattering phenomena continues to attract, perplex and challenge mathematicians from diverse disciplines. On the other hand problems in inverse scattering are non-linear and unstable.
This presentation is a journey through some new mathematical developments related to direct and inverse scattering theory for inhomogeneous media. Particular emphasis will be given to  three spectral sets that intrinsically appear in the study of the relative scattering operator, namely scattering poles, non-scattering frequencies and transmission eigenvalues. We show how the  understanding  of these sets guides us to extract nonlinear information about the inhomogeneity from the linear relative scattering operator. Related examples of reconstructions will be presented.
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