turkmath.org

Laplacian operators on graphs have a long history and enjoy deep connections to numerous branches of mathematics and mathematical physics. Laplacians on metric graphs, which are also widely known as quantum graphs, got a lot of attention during the last decades as simplified models of complicated quantum systems. The main focus in this talk will be on the self-adjointness problem (a.k.a. quantum completeness) for the corresponding Laplacian. More specifically, we will discuss the relationship between one of the classical notions of boundaries for infinite graphs, graph ends, and self-adjoint extensions of the minimal Kirchhoff Laplacian on a metric graph. The talk is based on joint works with D. Mugnolo (FernUni Hagen) and N. Nicolussi (TU Graz).