Speaker
Description
We consider Laplacians on periodic discrete graphs. Their spectrum consists of a finite number of bands. We obtain two-sided estimates for the total length of the spectral bands of the Laplacian in terms of geometric parameters of the graph. Moreover, we consider Schr\"odinger operators with periodic potentials on periodic discrete graphs. We obtain two-sided estimates for the total length of the spectral bands of the operators in terms of geometric parameters of the graph and the potential. The proof is based on the Floquet theory and the trace formulas for fiber operators. In particular, we show that these estimates are sharp. It means that these estimates become identities for specific graphs and potentials. Joint work with N.Saburova
