Sergei Avdonin: Inverse Problems for Differential Equations on Graphs

The inverse problem consists in reconstructing the metric graph, differential operator on its edges and matching conditions at the internal vertices from spectral or dynamical data. In this talk we describe the leaf-peeling method which combines spectral and dynamical approaches to inverse problems for differential equations on graphs and develops a constructive procedure for the recovery of graphs parameters. This procedures is recursive — it allows recalculating the inverse data from the original graph to smaller graphs. The method is demonstrated for the wave, heat and Schrödinger equations on graphs. The talk is based in part on joint work with Pavel Kurasov.