Talk by Sergei Avdonin
On May 3rd, 2023, Sergei Avdonin (University of Alaska Fairbanks, United States) gave a talk about "Inverse Problems for the Dirac Equation on Metric Graphs" as part of the online workshop on "Dirac equation between discrete and continuous: new trends and applications" organized by Ginestra Bianconi (Queen Mary University of London) and Delio Mugnolo (FernUniversität in Hagen). This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
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We consider inverse spectral and dynamic problems for a one-dimensional Dirac system on finite metric graphs. Our goal is to recover the topology (connectivity) of the graph, lengths of the edges, and a matrix potential on each edge. First we consider trees, i.e. graphs without cycles, and then discuss how to extend our approach to general graphs. We use the Weyl matrix function or the dynamic response operator as the inverse data and apply a new version of the leaf peeling method, which was originally developed for the wave and Schr¨odinger equation on tree graphs. We also present a new dynamic algorithm to solve the forward problem for the Dirac system on general finite metric graphs. The talk is based in part on joint work with Nina Avdonina and Olha Sus.
