Recent progress made in different advanced topics of physics and emerging nano-, and quantum- technology caused appearance of several challenging problems in mathematical physics of PDE and spectral theory of differential operators having applications in physics. Broad variety of challenging mathematical problems arising in condensed matter physics, quantum materials, nonlinear optics, physics of matter waves and PT-symmetric physics will be discussed in invited and plenary talks by the speakers.
Lectures in summer schools will be presented in the form of short tutorial courses and will cover spectral theory of quantum graphs and branched thin manifolds, evolution equations on metric graphs and nonlinear waves and solitons dynamics in networks. Auditorioum of the School will contain students, postdocs and young research associates working on mathematical physics, functional analysis, theoretical condensed matter physics, quantum and nonlinear optics.