Pavel Kurasov: How can magnetic field help to solve inverse problems for quantum graphs

Inverse problems for quantum graphs with cycles can be solved using spectral data dependent on the flux of the magnetic field through the cycles. The solution is not unique if the system possesses certain symmetries. Some of these symmetries are straightforward, but some are hidden and appear as a result of analysis. Hidden symmetries can sometimes be given clear interpretation in spectral terms or in terms of scattering matrix. Our focus will be on hidden symmetries of vertex matching conditions.