Oleg Safronov, UNC Charlotte
Title: Localization on quantum graphs.
Abstract: I would give some basic definitions that are needed to understand what a localization is. One needs to define such notions as pure point spectrum and how could it be dense in some intervals. The localization will be discussed for the random Schrodinger operator on the graph defined as the union of intervals of length 1 connecting points of the lattice Z^d. The vertices of this graph are called “junctions”. Randomness of properties of “junctions” will cause the particles or waves with certain energies to localize (i.e. to be trapped) in the corresponding medium.