22 September at 12:00 MSK
Quantum graphs with infinitely many vertices and edges will be discussed. We do not assume that there is a positive lower bound on the lengths of its edges. Our main result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection we will discuss spectral properties of infinite quantum graphs (several self-adjointness results, the problem of lower semiboundedness, spectral estimates, and spectral types).
Professor Malamud Mark M., RUDN, Moscow.
Topic: To the Spectral Theory of Infinite Quantum Graphs.