PDEs, MP and HA Seminar, Friday 11th April 2008, 1.50pm, Bloc 627

Title: Making fat graphs, in particular bent Dirichlet tubes, lean.
Author: Pavel Exner, Doppler Institute for Mathematical Physics
        and Applied Mathematics, Prague

Abstract:
The problem discussed in this talk is motivated by eŽorts to understand ap-
proximation of quantum graph Hamiltonians by Laplacians on families of \fat
graphs". The emphasis is on new results in the Dirichlet case, however, ¯rst
we review the background and explain the importance of vertex boundary
conditions using a lattice graph example, and mention known result in both
the Neumann and Dirichlet setting. After that we suggest a way how wider
classes of vertex couplings can be obtained from squeezed Dirichlet networks.
To illustrate the proposed strategy we work out the simplest nontrivial ex-
ample, a family of bent tubes giving a graph of one vertex and two edges, or
a two-parameter family of generalized point interactions on the line.