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Pavel Kurasov: Peeling-breaking-breaking-peeling... Inverse problem for quantum graphs

Time: Wed 2019-05-08 13.15 - 14.15

Location: Room 34, House 6, Kräftriket, Department of Mathematics, Stockholm University

Lecturer: Pavel Kurasov, SU


We are going to present solution of the inverse problem for quantum graphs --Schr\"odinger operators on metric graphs. The set of spectral data consists essentially of the matrix analog of Titchmarsh-Weyl $ M$-function associated with graph's boundary and depends on the magnetic fluxes through the cycles. Solution to the problem is obtained by combining {\bf peeling} of edges with {\bf breaking} of cycles. The method is based on detailed analysis of invisible eigenfunctions -- those eigenfunctions that cannot be detected from the boundary observations.